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Algebra 2 Flashcards: Factor Quadratics To Find Zeros

Study Factor Quadratics To Find Zeros in Algebra 2 with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

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What this deck covers

This deck focuses on Factor Quadratics To Find Zeros, 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: Factor Quadratics To Find Zeros

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QUESTION

What is the factored form of 2x2+7x+32x^2+7x+32x2+7x+3?

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ANSWER

(2x+1)(x+3)(2x+1)(x+3)(2x+1)(x+3). Use AC method: 2⋅3=62 \cdot 3 = 62⋅3=6, factors 111 and 666 add to 777.

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Flashcard 1: What is the factored form of 2x2+7x+32x^2+7x+32x2+7x+3?

Answer: (2x+1)(x+3)(2x+1)(x+3)(2x+1)(x+3). Use AC method: 2⋅3=62 \cdot 3 = 62⋅3=6, factors 111 and 666 add to 777.

Flashcard 2: What are the zeros of f(x)=(x−4)(x−5)f(x)=(x-4)(x-5)f(x)=(x−4)(x−5)?

Answer: x=4,5x=4,5x=4,5. Set each factor equal to zero: x−4=0x-4=0x−4=0 or x−5=0x-5=0x−5=0.

Flashcard 3: What is the factored form of x2+6x+9x^2+6x+9x2+6x+9?

Answer: (x+3)2(x+3)^2(x+3)2. Perfect square trinomial: x2+6x+9=(x+3)2x^2+6x+9=(x+3)^2x2+6x+9=(x+3)2.

Flashcard 4: What are the zeros of f(x)=x2−16f(x)=x^2-16f(x)=x2−16?

Answer: x=4,−4x=4,-4x=4,−4. From factored form x2−16=(x−4)(x+4)x^2-16=(x-4)(x+4)x2−16=(x−4)(x+4).

Flashcard 5: What are the zeros of f(x)=3x2−10x−8f(x)=3x^2-10x-8f(x)=3x2−10x−8?

Answer: x=−23,4x=-\frac{2}{3},4x=−32​,4. From factored form 3x2−10x−8=(3x+2)(x−4)3x^2-10x-8=(3x+2)(x-4)3x2−10x−8=(3x+2)(x−4).

Flashcard 6: What is the factored form of x2+x−12x^2+x-12x2+x−12?

Answer: (x+4)(x−3)(x+4)(x-3)(x+4)(x−3). Find two numbers that multiply to −12-12−12 and add to 111: 444 and −3-3−3.

Flashcard 7: What is the factored form of x2+7x+12x^2+7x+12x2+7x+12?

Answer: (x+3)(x+4)(x+3)(x+4)(x+3)(x+4). Find two numbers that multiply to 121212 and add to 777: 333 and 444.

Flashcard 8: What are the zeros of f(x)=(x−5)(x+2)f(x)=(x-5)(x+2)f(x)=(x−5)(x+2)?

Answer: x=5,−2x=5,-2x=5,−2. Set each factor equal to zero: x−5=0x-5=0x−5=0 or x+2=0x+2=0x+2=0.

Flashcard 9: What is the relationship between factors and zeros for f(x)=(x−r)(x−s)f(x)=(x-r)(x-s)f(x)=(x−r)(x−s)?

Answer: Zeros are x=rx=rx=r and x=sx=sx=s. When (x−r)=0(x-r)=0(x−r)=0 then x=rx=rx=r, and when (x−s)=0(x-s)=0(x−s)=0 then x=sx=sx=s.

Flashcard 10: What is the factored form of x2−9x^2-9x2−9?

Answer: (x−3)(x+3)(x-3)(x+3)(x−3)(x+3). Difference of squares: a2−b2=(a−b)(a+b)a^2-b^2=(a-b)(a+b)a2−b2=(a−b)(a+b).

Flashcard 11: What are the zeros of f(x)=x2−9f(x)=x^2-9f(x)=x2−9?

Answer: x=3,−3x=3,-3x=3,−3. Set each factor equal to zero: x=3x=3x=3 or x=−3x=-3x=−3.

Flashcard 12: What is the factored form of x2−5x+6x^2-5x+6x2−5x+6?

Answer: (x−2)(x−3)(x-2)(x-3)(x−2)(x−3). Find two numbers that multiply to 666 and add to −5-5−5: −2-2−2 and −3-3−3.

Flashcard 13: What are the zeros of f(x)=x2−5x+6f(x)=x^2-5x+6f(x)=x2−5x+6?

Answer: x=2,3x=2,3x=2,3. From factored form x2−5x+6=(x−2)(x−3)x^2-5x+6=(x-2)(x-3)x2−5x+6=(x−2)(x−3).

Flashcard 14: What is the factored form of x2+2x−15x^2+2x-15x2+2x−15?

Answer: (x+5)(x−3)(x+5)(x-3)(x+5)(x−3). Find two numbers that multiply to −15-15−15 and add to 222: 555 and −3-3−3.

Flashcard 15: What are the zeros of f(x)=(x+5)(x−3)f(x)=(x+5)(x-3)f(x)=(x+5)(x−3)?

Answer: x=−5,3x=-5,3x=−5,3. Set each factor equal to zero: x+5=0x+5=0x+5=0 or x−3=0x-3=0x−3=0.

Flashcard 16: What is the factored form of x2−2x−8x^2-2x-8x2−2x−8?

Answer: (x−4)(x+2)(x-4)(x+2)(x−4)(x+2). Find two numbers that multiply to −8-8−8 and add to −2-2−2: −4-4−4 and 222.

Flashcard 17: What is the factored form of x2+11x+24x^2+11x+24x2+11x+24?

Answer: (x+3)(x+8)(x+3)(x+8)(x+3)(x+8). Find two numbers that multiply to 242424 and add to 111111: 333 and 888.

Flashcard 18: What are the zeros of f(x)=(x+3)(x+8)f(x)=(x+3)(x+8)f(x)=(x+3)(x+8)?

Answer: x=−3,−8x=-3,-8x=−3,−8. Set each factor equal to zero: x+3=0x+3=0x+3=0 or x+8=0x+8=0x+8=0.

Flashcard 19: What is the factored form of x2−11x+24x^2-11x+24x2−11x+24?

Answer: (x−3)(x−8)(x-3)(x-8)(x−3)(x−8). Find two numbers that multiply to 242424 and add to −11-11−11: −3-3−3 and −8-8−8.

Flashcard 20: What are the zeros of f(x)=x2−11x+24f(x)=x^2-11x+24f(x)=x2−11x+24?

Answer: x=3,8x=3,8x=3,8. From factored form x2−11x+24=(x−3)(x−8)x^2-11x+24=(x-3)(x-8)x2−11x+24=(x−3)(x−8).

Flashcard 21: What is the factored form of x2+9x+20x^2+9x+20x2+9x+20?

Answer: (x+4)(x+5)(x+4)(x+5)(x+4)(x+5). Find two numbers that multiply to 202020 and add to 999: 444 and 555.

Flashcard 22: What is the factored form of x2−9x+20x^2-9x+20x2−9x+20?

Answer: (x−4)(x−5)(x-4)(x-5)(x−4)(x−5). Find two numbers that multiply to 202020 and add to −9-9−9: −4-4−4 and −5-5−5.

Flashcard 23: What is the factored form of x2−13x+36x^2-13x+36x2−13x+36?

Answer: (x−4)(x−9)(x-4)(x-9)(x−4)(x−9). Find two numbers that multiply to 363636 and add to −13-13−13: −4-4−4 and −9-9−9.

Flashcard 24: What are the zeros of f(x)=x2−13x+36f(x)=x^2-13x+36f(x)=x2−13x+36?

Answer: x=4,9x=4,9x=4,9. From factored form x2−13x+36=(x−4)(x−9)x^2-13x+36=(x-4)(x-9)x2−13x+36=(x−4)(x−9).

Flashcard 25: What is the factored form of x2+13x+36x^2+13x+36x2+13x+36?

Answer: (x+4)(x+9)(x+4)(x+9)(x+4)(x+9). Find two numbers that multiply to 363636 and add to 131313: 444 and 999.

Flashcard 26: What is the factored form of x2−4x−21x^2-4x-21x2−4x−21?

Answer: (x−7)(x+3)(x-7)(x+3)(x−7)(x+3). Find two numbers that multiply to −21-21−21 and add to −4-4−4: −7-7−7 and 333.

Flashcard 27: What are the zeros of f(x)=(x−7)(x+3)f(x)=(x-7)(x+3)f(x)=(x−7)(x+3)?

Answer: x=7,−3x=7,-3x=7,−3. Set each factor equal to zero: x−7=0x-7=0x−7=0 or x+3=0x+3=0x+3=0.

Flashcard 28: What is the factored form of x2+4x−21x^2+4x-21x2+4x−21?

Answer: (x+7)(x−3)(x+7)(x-3)(x+7)(x−3). Find two numbers that multiply to −21-21−21 and add to 444: 777 and −3-3−3.

Flashcard 29: What is the factored form of x2−6x+9x^2-6x+9x2−6x+9?

Answer: (x−3)2(x-3)^2(x−3)2. Perfect square trinomial: x2−6x+9=(x−3)2x^2-6x+9=(x-3)^2x2−6x+9=(x−3)2.

Flashcard 30: What is the zero (with multiplicity) of f(x)=(x−3)2f(x)=(x-3)^2f(x)=(x−3)2?

Answer: x=3x=3x=3 with multiplicity 222. A repeated factor gives a zero with multiplicity equal to the exponent.