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Algebra 2 Flashcards: Applying The Remainder Theorem

Study Applying The Remainder Theorem in Algebra 2 with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Applying The Remainder Theorem, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Algebra 2 Flashcards: Applying The Remainder Theorem

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

If $p(-4)=12$ , what is the remainder when dividing $p(x)$ by $x+4$ ?

Tap or drag to reveal answer

ANSWER

Remainder $=12$ . By the Remainder Theorem, the remainder equals $p(-4)$ .

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: If $p(-4)=12$ , what is the remainder when dividing $p(x)$ by $x+4$ ?

Answer: Remainder $=12$ . By the Remainder Theorem, the remainder equals $p(-4)$ .

Flashcard 2: Find the value of $k$ so that $x-2$ is a factor of $p(x)=x^2+kx-6$ .

Answer: $k=1$ . Set $p(2)=0$ : $4+2k-6=0$ , so $k=1$ .

Flashcard 3: Find the value of $k$ so that $x+3$ is a factor of $p(x)=2x^2+kx-9$ .

Answer: $k=3$ . Set $p(-3)=0$ : $18-3k-9=0$ , so $k=3$ .

Flashcard 4: Find the value of $k$ so that $x-1$ is a factor of $p(x)=x^3-4x^2+kx+3$ .

Answer: $k=0$ . Set $p(1)=0$ : $1-4+k+3=0$ , so $k=0$ .

Flashcard 5: What is the remainder when dividing $p(x)=x^3+2x^2-x-2$ by $x-1$ ?

Answer: $p(1)=0$ . Calculate $p(1)=1^3+2(1)^2-1-2=1+2-1-2=0$ .

Flashcard 6: What is the remainder when dividing $p(x)=x^3+2x^2-x-2$ by $x+2$ ?

Answer: $p(-2)=0$ . Calculate $p(-2)=(-2)^3+2(-2)^2-(-2)-2=-8+8+2-2=0$ .

Flashcard 7: What is the remainder when dividing $p(x)=x^3-2x^2+x-2$ by $x-2$ ?

Answer: $p(2)=0$ . Calculate $p(2)=8-8+2-2=0$ .

Flashcard 8: What is the remainder when dividing $p(x)=x^3-2x^2+x-2$ by $x+1$ ?

Answer: $p(-1)=-6$ . Calculate $p(-1)=-1-2-1-2=-6$ .

Flashcard 9: Which statement is true if the remainder on division by $x-4$ is $0$ ?

Answer: $(x-4)$ is a factor of $p(x)$ . A zero remainder means the divisor is a factor.

Flashcard 10: What does the Remainder Theorem state for the remainder when dividing $p(x)$ by $x-a$ ?

Answer: Remainder $=p(a)$ . This is the core statement of the Remainder Theorem.

Flashcard 11: What is the remainder when dividing $p(x)$ by $x-3$ in terms of $p$ ?

Answer: Remainder $=p(3)$ . By the Remainder Theorem, substitute $a=3$ .

Flashcard 12: What is the remainder when dividing $p(x)$ by $x+5$ in terms of $p$ ?

Answer: Remainder $=p(-5)$ . Since $x+5=x-(-5)$ , we have $a=-5$ .

Flashcard 13: What does the Factor Theorem state using $p(a)$ and the factor $(x-a)$ ?

Answer: $p(a)=0\iff (x-a)$ is a factor of $p(x)$ . The Factor Theorem combines remainder and factorization.

Flashcard 14: Which condition guarantees that $(x-a)$ is a factor of $p(x)$ : $p(a)=0$ or $p(a)\neq 0$ ?

Answer: $p(a)=0$ . When $p(a)=0$ , the remainder is zero, making $(x-a)$ a factor.

Flashcard 15: If $(x-a)$ is a factor of $p(x)$ , what must the remainder be when dividing by $(x-a)$ ?

Answer: Remainder $=0$ . If $(x-a)$ is a factor, then $p(a)=0$ .

Flashcard 16: Identify the value of $a$ used in the Remainder Theorem when the divisor is $x-7$ .

Answer: $a=7$ . For divisor $x-7$ , the value $a=7$ .

Flashcard 17: Identify the value of $a$ used in the Remainder Theorem when the divisor is $x+7$ .

Answer: $a=-7$ . For divisor $x+7=x-(-7)$ , the value $a=-7$ .

Flashcard 18: What is the remainder when dividing $p(x)=x^3-4x+1$ by $x-2$ ?

Answer: $p(2)=1$ . Calculate $p(2)=2^3-4(2)+1=8-8+1=1$ .

Flashcard 19: What is the remainder when dividing $p(x)=x^2+3x-10$ by $x-2$ ?

Answer: $p(2)=0$ . Calculate $p(2)=2^2+3(2)-10=4+6-10=0$ .

Flashcard 20: What is the remainder when dividing $p(x)=x^2+3x-10$ by $x+5$ ?

Answer: $p(-5)=0$ . Calculate $p(-5)=(-5)^2+3(-5)-10=25-15-10=0$ .

Flashcard 21: What is the remainder when dividing $p(x)=2x^3-x^2+5$ by $x-1$ ?

Answer: $p(1)=6$ . Calculate $p(1)=2(1)^3-(1)^2+5=2-1+5=6$ .

Flashcard 22: What is the remainder when dividing $p(x)=2x^3-x^2+5$ by $x+1$ ?

Answer: $p(-1)=2$ . Calculate $p(-1)=2(-1)^3-(-1)^2+5=-2-1+5=2$ .

Flashcard 23: What is the remainder when dividing $p(x)=x^4-16$ by $x-2$ ?

Answer: $p(2)=0$ . Calculate $p(2)=2^4-16=16-16=0$ .

Flashcard 24: What is the remainder when dividing $p(x)=x^4-16$ by $x+2$ ?

Answer: $p(-2)=0$ . Calculate $p(-2)=(-2)^4-16=16-16=0$ .

Flashcard 25: If the remainder on division by $x-a$ is $r$ , what is $p(a)$ equal to?

Answer: $p(a)=r$ . The remainder equals the polynomial evaluated at $a$ .

Flashcard 26: If $p(6)=-3$ , what is the remainder when dividing $p(x)$ by $x-6$ ?

Answer: Remainder $=-3$ . By the Remainder Theorem, the remainder equals $p(6)$ .

Flashcard 27: If $p(0)=5$ , what is the remainder when dividing $p(x)$ by $x$ ?

Answer: Remainder $=5$ . Dividing by $x$ means evaluating at $x=0$ .

Flashcard 28: What is the remainder when dividing $p(x)=3x^2-12x+9$ by $x-1$ ?

Answer: $p(1)=0$ . Calculate $p(1)=3(1)^2-12(1)+9=3-12+9=0$ .

Flashcard 29: Find the value of $k$ so that $x+2$ is a factor of $p(x)=x^3+kx^2-4x+8$ .

Answer: $k=0$ . Set $p(-2)=0$ : $-8+4k+8+8=0$ , so $k=0$ .

Flashcard 30: What is the remainder when dividing $p(x)=3x^2-12x+9$ by $x-3$ ?

Answer: $p(3)=0$ . Calculate $p(3)=3(3)^2-12(3)+9=27-36+9=0$ .

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Algebra 2 Flashcards: Applying The Remainder Theorem

Study Applying The Remainder Theorem in Algebra 2 with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Applying The Remainder Theorem, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Algebra 2 Flashcards: Applying The Remainder Theorem

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

If $p(-4)=12$ , what is the remainder when dividing $p(x)$ by $x+4$ ?

Tap or drag to reveal answer

ANSWER

Remainder $=12$ . By the Remainder Theorem, the remainder equals $p(-4)$ .

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: If $p(-4)=12$ , what is the remainder when dividing $p(x)$ by $x+4$ ?

Answer: Remainder $=12$ . By the Remainder Theorem, the remainder equals $p(-4)$ .

Flashcard 2: Find the value of $k$ so that $x-2$ is a factor of $p(x)=x^2+kx-6$ .

Answer: $k=1$ . Set $p(2)=0$ : $4+2k-6=0$ , so $k=1$ .

Flashcard 3: Find the value of $k$ so that $x+3$ is a factor of $p(x)=2x^2+kx-9$ .

Answer: $k=3$ . Set $p(-3)=0$ : $18-3k-9=0$ , so $k=3$ .

Flashcard 4: Find the value of $k$ so that $x-1$ is a factor of $p(x)=x^3-4x^2+kx+3$ .

Answer: $k=0$ . Set $p(1)=0$ : $1-4+k+3=0$ , so $k=0$ .

Flashcard 5: What is the remainder when dividing $p(x)=x^3+2x^2-x-2$ by $x-1$ ?

Answer: $p(1)=0$ . Calculate $p(1)=1^3+2(1)^2-1-2=1+2-1-2=0$ .

Flashcard 6: What is the remainder when dividing $p(x)=x^3+2x^2-x-2$ by $x+2$ ?

Answer: $p(-2)=0$ . Calculate $p(-2)=(-2)^3+2(-2)^2-(-2)-2=-8+8+2-2=0$ .

Flashcard 7: What is the remainder when dividing $p(x)=x^3-2x^2+x-2$ by $x-2$ ?

Answer: $p(2)=0$ . Calculate $p(2)=8-8+2-2=0$ .

Flashcard 8: What is the remainder when dividing $p(x)=x^3-2x^2+x-2$ by $x+1$ ?

Answer: $p(-1)=-6$ . Calculate $p(-1)=-1-2-1-2=-6$ .

Flashcard 9: Which statement is true if the remainder on division by $x-4$ is $0$ ?

Answer: $(x-4)$ is a factor of $p(x)$ . A zero remainder means the divisor is a factor.

Flashcard 10: What does the Remainder Theorem state for the remainder when dividing $p(x)$ by $x-a$ ?

Answer: Remainder $=p(a)$ . This is the core statement of the Remainder Theorem.

Flashcard 11: What is the remainder when dividing $p(x)$ by $x-3$ in terms of $p$ ?

Answer: Remainder $=p(3)$ . By the Remainder Theorem, substitute $a=3$ .

Flashcard 12: What is the remainder when dividing $p(x)$ by $x+5$ in terms of $p$ ?

Answer: Remainder $=p(-5)$ . Since $x+5=x-(-5)$ , we have $a=-5$ .

Flashcard 13: What does the Factor Theorem state using $p(a)$ and the factor $(x-a)$ ?

Answer: $p(a)=0\iff (x-a)$ is a factor of $p(x)$ . The Factor Theorem combines remainder and factorization.

Flashcard 14: Which condition guarantees that $(x-a)$ is a factor of $p(x)$ : $p(a)=0$ or $p(a)\neq 0$ ?

Answer: $p(a)=0$ . When $p(a)=0$ , the remainder is zero, making $(x-a)$ a factor.

Flashcard 15: If $(x-a)$ is a factor of $p(x)$ , what must the remainder be when dividing by $(x-a)$ ?

Answer: Remainder $=0$ . If $(x-a)$ is a factor, then $p(a)=0$ .

Flashcard 16: Identify the value of $a$ used in the Remainder Theorem when the divisor is $x-7$ .

Answer: $a=7$ . For divisor $x-7$ , the value $a=7$ .

Flashcard 17: Identify the value of $a$ used in the Remainder Theorem when the divisor is $x+7$ .

Answer: $a=-7$ . For divisor $x+7=x-(-7)$ , the value $a=-7$ .

Flashcard 18: What is the remainder when dividing $p(x)=x^3-4x+1$ by $x-2$ ?

Answer: $p(2)=1$ . Calculate $p(2)=2^3-4(2)+1=8-8+1=1$ .

Flashcard 19: What is the remainder when dividing $p(x)=x^2+3x-10$ by $x-2$ ?

Answer: $p(2)=0$ . Calculate $p(2)=2^2+3(2)-10=4+6-10=0$ .

Flashcard 20: What is the remainder when dividing $p(x)=x^2+3x-10$ by $x+5$ ?

Answer: $p(-5)=0$ . Calculate $p(-5)=(-5)^2+3(-5)-10=25-15-10=0$ .

Flashcard 21: What is the remainder when dividing $p(x)=2x^3-x^2+5$ by $x-1$ ?

Answer: $p(1)=6$ . Calculate $p(1)=2(1)^3-(1)^2+5=2-1+5=6$ .

Flashcard 22: What is the remainder when dividing $p(x)=2x^3-x^2+5$ by $x+1$ ?

Answer: $p(-1)=2$ . Calculate $p(-1)=2(-1)^3-(-1)^2+5=-2-1+5=2$ .

Flashcard 23: What is the remainder when dividing $p(x)=x^4-16$ by $x-2$ ?

Answer: $p(2)=0$ . Calculate $p(2)=2^4-16=16-16=0$ .

Flashcard 24: What is the remainder when dividing $p(x)=x^4-16$ by $x+2$ ?

Answer: $p(-2)=0$ . Calculate $p(-2)=(-2)^4-16=16-16=0$ .

Flashcard 25: If the remainder on division by $x-a$ is $r$ , what is $p(a)$ equal to?

Answer: $p(a)=r$ . The remainder equals the polynomial evaluated at $a$ .

Flashcard 26: If $p(6)=-3$ , what is the remainder when dividing $p(x)$ by $x-6$ ?

Answer: Remainder $=-3$ . By the Remainder Theorem, the remainder equals $p(6)$ .

Flashcard 27: If $p(0)=5$ , what is the remainder when dividing $p(x)$ by $x$ ?

Answer: Remainder $=5$ . Dividing by $x$ means evaluating at $x=0$ .

Flashcard 28: What is the remainder when dividing $p(x)=3x^2-12x+9$ by $x-1$ ?

Answer: $p(1)=0$ . Calculate $p(1)=3(1)^2-12(1)+9=3-12+9=0$ .

Flashcard 29: Find the value of $k$ so that $x+2$ is a factor of $p(x)=x^3+kx^2-4x+8$ .

Answer: $k=0$ . Set $p(-2)=0$ : $-8+4k+8+8=0$ , so $k=0$ .

Flashcard 30: What is the remainder when dividing $p(x)=3x^2-12x+9$ by $x-3$ ?

Answer: $p(3)=0$ . Calculate $p(3)=3(3)^2-12(3)+9=27-36+9=0$ .

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Algebra 2 Flashcards: Applying The Remainder Theorem

What this deck covers

How to use these flashcards

Algebra 2 Flashcards: Applying The Remainder Theorem

All flashcards

Flashcard 1: If p(−4)=12p(-4)=12p(−4)=12, what is the remainder when dividing p(x)p(x)p(x) by x+4x+4x+4?

Flashcard 2: Find the value of kkk so that x−2x-2x−2 is a factor of p(x)=x2+kx−6p(x)=x^2+kx-6p(x)=x2+kx−6.

Flashcard 3: Find the value of kkk so that x+3x+3x+3 is a factor of p(x)=2x2+kx−9p(x)=2x^2+kx-9p(x)=2x2+kx−9.

Flashcard 4: Find the value of kkk so that x−1x-1x−1 is a factor of p(x)=x3−4x2+kx+3p(x)=x^3-4x^2+kx+3p(x)=x3−4x2+kx+3.

Flashcard 5: What is the remainder when dividing p(x)=x3+2x2−x−2p(x)=x^3+2x^2-x-2p(x)=x3+2x2−x−2 by x−1x-1x−1?

Flashcard 6: What is the remainder when dividing p(x)=x3+2x2−x−2p(x)=x^3+2x^2-x-2p(x)=x3+2x2−x−2 by x+2x+2x+2?

Flashcard 7: What is the remainder when dividing p(x)=x3−2x2+x−2p(x)=x^3-2x^2+x-2p(x)=x3−2x2+x−2 by x−2x-2x−2?

Flashcard 8: What is the remainder when dividing p(x)=x3−2x2+x−2p(x)=x^3-2x^2+x-2p(x)=x3−2x2+x−2 by x+1x+1x+1?

Flashcard 9: Which statement is true if the remainder on division by x−4x-4x−4 is 000?

Flashcard 10: What does the Remainder Theorem state for the remainder when dividing p(x)p(x)p(x) by x−ax-ax−a?

Flashcard 11: What is the remainder when dividing p(x)p(x)p(x) by x−3x-3x−3 in terms of ppp?

Flashcard 12: What is the remainder when dividing p(x)p(x)p(x) by x+5x+5x+5 in terms of ppp?

Flashcard 13: What does the Factor Theorem state using p(a)p(a)p(a) and the factor (x−a)(x-a)(x−a)?

Flashcard 14: Which condition guarantees that (x−a)(x-a)(x−a) is a factor of p(x)p(x)p(x): p(a)=0p(a)=0p(a)=0 or p(a)≠0p(a)\neq 0p(a)=0?

Flashcard 15: If (x−a)(x-a)(x−a) is a factor of p(x)p(x)p(x), what must the remainder be when dividing by (x−a)(x-a)(x−a)?

Flashcard 16: Identify the value of aaa used in the Remainder Theorem when the divisor is x−7x-7x−7.

Flashcard 17: Identify the value of aaa used in the Remainder Theorem when the divisor is x+7x+7x+7.

Flashcard 18: What is the remainder when dividing p(x)=x3−4x+1p(x)=x^3-4x+1p(x)=x3−4x+1 by x−2x-2x−2?

Flashcard 19: What is the remainder when dividing p(x)=x2+3x−10p(x)=x^2+3x-10p(x)=x2+3x−10 by x−2x-2x−2?

Flashcard 20: What is the remainder when dividing p(x)=x2+3x−10p(x)=x^2+3x-10p(x)=x2+3x−10 by x+5x+5x+5?

Flashcard 21: What is the remainder when dividing p(x)=2x3−x2+5p(x)=2x^3-x^2+5p(x)=2x3−x2+5 by x−1x-1x−1?

Flashcard 22: What is the remainder when dividing p(x)=2x3−x2+5p(x)=2x^3-x^2+5p(x)=2x3−x2+5 by x+1x+1x+1?

Flashcard 23: What is the remainder when dividing p(x)=x4−16p(x)=x^4-16p(x)=x4−16 by x−2x-2x−2?

Flashcard 24: What is the remainder when dividing p(x)=x4−16p(x)=x^4-16p(x)=x4−16 by x+2x+2x+2?

Flashcard 25: If the remainder on division by x−ax-ax−a is rrr, what is p(a)p(a)p(a) equal to?

Flashcard 26: If p(6)=−3p(6)=-3p(6)=−3, what is the remainder when dividing p(x)p(x)p(x) by x−6x-6x−6?

Flashcard 27: If p(0)=5p(0)=5p(0)=5, what is the remainder when dividing p(x)p(x)p(x) by xxx?

Flashcard 28: What is the remainder when dividing p(x)=3x2−12x+9p(x)=3x^2-12x+9p(x)=3x2−12x+9 by x−1x-1x−1?

Flashcard 29: Find the value of kkk so that x+2x+2x+2 is a factor of p(x)=x3+kx2−4x+8p(x)=x^3+kx^2-4x+8p(x)=x3+kx2−4x+8.

Flashcard 30: What is the remainder when dividing p(x)=3x2−12x+9p(x)=3x^2-12x+9p(x)=3x2−12x+9 by x−3x-3x−3?

Opening subject page...

Algebra 2 Flashcards: Applying The Remainder Theorem

What this deck covers

How to use these flashcards

Algebra 2 Flashcards: Applying The Remainder Theorem

All flashcards

Flashcard 1: If p(−4)=12p(-4)=12p(−4)=12, what is the remainder when dividing p(x)p(x)p(x) by x+4x+4x+4?

Flashcard 2: Find the value of kkk so that x−2x-2x−2 is a factor of p(x)=x2+kx−6p(x)=x^2+kx-6p(x)=x2+kx−6.

Flashcard 3: Find the value of kkk so that x+3x+3x+3 is a factor of p(x)=2x2+kx−9p(x)=2x^2+kx-9p(x)=2x2+kx−9.

Flashcard 4: Find the value of kkk so that x−1x-1x−1 is a factor of p(x)=x3−4x2+kx+3p(x)=x^3-4x^2+kx+3p(x)=x3−4x2+kx+3.

Flashcard 5: What is the remainder when dividing p(x)=x3+2x2−x−2p(x)=x^3+2x^2-x-2p(x)=x3+2x2−x−2 by x−1x-1x−1?

Flashcard 6: What is the remainder when dividing p(x)=x3+2x2−x−2p(x)=x^3+2x^2-x-2p(x)=x3+2x2−x−2 by x+2x+2x+2?

Flashcard 7: What is the remainder when dividing p(x)=x3−2x2+x−2p(x)=x^3-2x^2+x-2p(x)=x3−2x2+x−2 by x−2x-2x−2?

Flashcard 8: What is the remainder when dividing p(x)=x3−2x2+x−2p(x)=x^3-2x^2+x-2p(x)=x3−2x2+x−2 by x+1x+1x+1?

Flashcard 9: Which statement is true if the remainder on division by x−4x-4x−4 is 000?

Flashcard 10: What does the Remainder Theorem state for the remainder when dividing p(x)p(x)p(x) by x−ax-ax−a?

Flashcard 11: What is the remainder when dividing p(x)p(x)p(x) by x−3x-3x−3 in terms of ppp?

Flashcard 12: What is the remainder when dividing p(x)p(x)p(x) by x+5x+5x+5 in terms of ppp?

Flashcard 13: What does the Factor Theorem state using p(a)p(a)p(a) and the factor (x−a)(x-a)(x−a)?

Flashcard 14: Which condition guarantees that (x−a)(x-a)(x−a) is a factor of p(x)p(x)p(x): p(a)=0p(a)=0p(a)=0 or p(a)≠0p(a)\neq 0p(a)=0?

Flashcard 15: If (x−a)(x-a)(x−a) is a factor of p(x)p(x)p(x), what must the remainder be when dividing by (x−a)(x-a)(x−a)?

Flashcard 16: Identify the value of aaa used in the Remainder Theorem when the divisor is x−7x-7x−7.

Flashcard 17: Identify the value of aaa used in the Remainder Theorem when the divisor is x+7x+7x+7.

Flashcard 18: What is the remainder when dividing p(x)=x3−4x+1p(x)=x^3-4x+1p(x)=x3−4x+1 by x−2x-2x−2?

Flashcard 19: What is the remainder when dividing p(x)=x2+3x−10p(x)=x^2+3x-10p(x)=x2+3x−10 by x−2x-2x−2?

Flashcard 20: What is the remainder when dividing p(x)=x2+3x−10p(x)=x^2+3x-10p(x)=x2+3x−10 by x+5x+5x+5?

Flashcard 21: What is the remainder when dividing p(x)=2x3−x2+5p(x)=2x^3-x^2+5p(x)=2x3−x2+5 by x−1x-1x−1?

Flashcard 22: What is the remainder when dividing p(x)=2x3−x2+5p(x)=2x^3-x^2+5p(x)=2x3−x2+5 by x+1x+1x+1?

Flashcard 23: What is the remainder when dividing p(x)=x4−16p(x)=x^4-16p(x)=x4−16 by x−2x-2x−2?

Flashcard 24: What is the remainder when dividing p(x)=x4−16p(x)=x^4-16p(x)=x4−16 by x+2x+2x+2?

Flashcard 25: If the remainder on division by x−ax-ax−a is rrr, what is p(a)p(a)p(a) equal to?

Flashcard 26: If p(6)=−3p(6)=-3p(6)=−3, what is the remainder when dividing p(x)p(x)p(x) by x−6x-6x−6?

Flashcard 27: If p(0)=5p(0)=5p(0)=5, what is the remainder when dividing p(x)p(x)p(x) by xxx?

Flashcard 28: What is the remainder when dividing p(x)=3x2−12x+9p(x)=3x^2-12x+9p(x)=3x2−12x+9 by x−1x-1x−1?

Flashcard 29: Find the value of kkk so that x+2x+2x+2 is a factor of p(x)=x3+kx2−4x+8p(x)=x^3+kx^2-4x+8p(x)=x3+kx2−4x+8.

Flashcard 30: What is the remainder when dividing p(x)=3x2−12x+9p(x)=3x^2-12x+9p(x)=3x2−12x+9 by x−3x-3x−3?

Flashcard 1: If $p(-4)=12$ , what is the remainder when dividing $p(x)$ by $x+4$ ?

Flashcard 2: Find the value of $k$ so that $x-2$ is a factor of $p(x)=x^2+kx-6$ .

Flashcard 3: Find the value of $k$ so that $x+3$ is a factor of $p(x)=2x^2+kx-9$ .

Flashcard 4: Find the value of $k$ so that $x-1$ is a factor of $p(x)=x^3-4x^2+kx+3$ .

Flashcard 5: What is the remainder when dividing $p(x)=x^3+2x^2-x-2$ by $x-1$ ?

Flashcard 6: What is the remainder when dividing $p(x)=x^3+2x^2-x-2$ by $x+2$ ?

Flashcard 7: What is the remainder when dividing $p(x)=x^3-2x^2+x-2$ by $x-2$ ?

Flashcard 8: What is the remainder when dividing $p(x)=x^3-2x^2+x-2$ by $x+1$ ?

Flashcard 9: Which statement is true if the remainder on division by $x-4$ is $0$ ?

Flashcard 10: What does the Remainder Theorem state for the remainder when dividing $p(x)$ by $x-a$ ?

Flashcard 11: What is the remainder when dividing $p(x)$ by $x-3$ in terms of $p$ ?

Flashcard 12: What is the remainder when dividing $p(x)$ by $x+5$ in terms of $p$ ?

Flashcard 13: What does the Factor Theorem state using $p(a)$ and the factor $(x-a)$ ?

Flashcard 14: Which condition guarantees that $(x-a)$ is a factor of $p(x)$ : $p(a)=0$ or $p(a)\neq 0$ ?

Flashcard 15: If $(x-a)$ is a factor of $p(x)$ , what must the remainder be when dividing by $(x-a)$ ?

Flashcard 16: Identify the value of $a$ used in the Remainder Theorem when the divisor is $x-7$ .

Flashcard 17: Identify the value of $a$ used in the Remainder Theorem when the divisor is $x+7$ .

Flashcard 18: What is the remainder when dividing $p(x)=x^3-4x+1$ by $x-2$ ?

Flashcard 19: What is the remainder when dividing $p(x)=x^2+3x-10$ by $x-2$ ?

Flashcard 20: What is the remainder when dividing $p(x)=x^2+3x-10$ by $x+5$ ?

Flashcard 21: What is the remainder when dividing $p(x)=2x^3-x^2+5$ by $x-1$ ?

Flashcard 22: What is the remainder when dividing $p(x)=2x^3-x^2+5$ by $x+1$ ?

Flashcard 23: What is the remainder when dividing $p(x)=x^4-16$ by $x-2$ ?

Flashcard 24: What is the remainder when dividing $p(x)=x^4-16$ by $x+2$ ?

Flashcard 25: If the remainder on division by $x-a$ is $r$ , what is $p(a)$ equal to?

Flashcard 26: If $p(6)=-3$ , what is the remainder when dividing $p(x)$ by $x-6$ ?

Flashcard 27: If $p(0)=5$ , what is the remainder when dividing $p(x)$ by $x$ ?

Flashcard 28: What is the remainder when dividing $p(x)=3x^2-12x+9$ by $x-1$ ?

Flashcard 29: Find the value of $k$ so that $x+2$ is a factor of $p(x)=x^3+kx^2-4x+8$ .

Flashcard 30: What is the remainder when dividing $p(x)=3x^2-12x+9$ by $x-3$ ?

Flashcard 1: If $p(-4)=12$ , what is the remainder when dividing $p(x)$ by $x+4$ ?

Flashcard 2: Find the value of $k$ so that $x-2$ is a factor of $p(x)=x^2+kx-6$ .

Flashcard 3: Find the value of $k$ so that $x+3$ is a factor of $p(x)=2x^2+kx-9$ .

Flashcard 4: Find the value of $k$ so that $x-1$ is a factor of $p(x)=x^3-4x^2+kx+3$ .

Flashcard 5: What is the remainder when dividing $p(x)=x^3+2x^2-x-2$ by $x-1$ ?

Flashcard 6: What is the remainder when dividing $p(x)=x^3+2x^2-x-2$ by $x+2$ ?

Flashcard 7: What is the remainder when dividing $p(x)=x^3-2x^2+x-2$ by $x-2$ ?

Flashcard 8: What is the remainder when dividing $p(x)=x^3-2x^2+x-2$ by $x+1$ ?

Flashcard 9: Which statement is true if the remainder on division by $x-4$ is $0$ ?

Flashcard 10: What does the Remainder Theorem state for the remainder when dividing $p(x)$ by $x-a$ ?

Flashcard 11: What is the remainder when dividing $p(x)$ by $x-3$ in terms of $p$ ?

Flashcard 12: What is the remainder when dividing $p(x)$ by $x+5$ in terms of $p$ ?

Flashcard 13: What does the Factor Theorem state using $p(a)$ and the factor $(x-a)$ ?

Flashcard 14: Which condition guarantees that $(x-a)$ is a factor of $p(x)$ : $p(a)=0$ or $p(a)\neq 0$ ?

Flashcard 15: If $(x-a)$ is a factor of $p(x)$ , what must the remainder be when dividing by $(x-a)$ ?

Flashcard 16: Identify the value of $a$ used in the Remainder Theorem when the divisor is $x-7$ .

Flashcard 17: Identify the value of $a$ used in the Remainder Theorem when the divisor is $x+7$ .

Flashcard 18: What is the remainder when dividing $p(x)=x^3-4x+1$ by $x-2$ ?

Flashcard 19: What is the remainder when dividing $p(x)=x^2+3x-10$ by $x-2$ ?

Flashcard 20: What is the remainder when dividing $p(x)=x^2+3x-10$ by $x+5$ ?

Flashcard 21: What is the remainder when dividing $p(x)=2x^3-x^2+5$ by $x-1$ ?

Flashcard 22: What is the remainder when dividing $p(x)=2x^3-x^2+5$ by $x+1$ ?

Flashcard 23: What is the remainder when dividing $p(x)=x^4-16$ by $x-2$ ?

Flashcard 24: What is the remainder when dividing $p(x)=x^4-16$ by $x+2$ ?

Flashcard 25: If the remainder on division by $x-a$ is $r$ , what is $p(a)$ equal to?

Flashcard 26: If $p(6)=-3$ , what is the remainder when dividing $p(x)$ by $x-6$ ?

Flashcard 27: If $p(0)=5$ , what is the remainder when dividing $p(x)$ by $x$ ?

Flashcard 28: What is the remainder when dividing $p(x)=3x^2-12x+9$ by $x-1$ ?

Flashcard 29: Find the value of $k$ so that $x+2$ is a factor of $p(x)=x^3+kx^2-4x+8$ .

Flashcard 30: What is the remainder when dividing $p(x)=3x^2-12x+9$ by $x-3$ ?