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.

Algebra 2

Factor Quadratics To Find Zeros

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QUESTION

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What are the zeros of $f(x)=x^2-13x+36$ ?

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ANSWER

$x=4,9$ . From factored form $x^2-13x+36=(x-4)(x-9)$ .

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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.

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Flashcard 1: What are the zeros of $f(x)=x^2-13x+36$ ?

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

Flashcard 2: What is the relationship between factors and zeros for $f(x)=(x-r)(x-s)$ ?

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

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

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

Flashcard 4: What are the zeros of $f(x)=2x^2-5x-3$ ?

Answer: $x=-\frac{1}{2},3$ . From factored form $2x^2-5x-3=(2x+1)(x-3)$ .

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

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

Flashcard 6: What is the factored form of $x^2+7x+12$ ?

Answer: $(x+3)(x+4)$ . Find two numbers that multiply to $12$ and add to $7$ : $3$ and $4$ .

Flashcard 7: What are the zeros of $f(x)=3x^2-10x-8$ ?

Answer: $x=-\frac{2}{3},4$ . From factored form $3x^2-10x-8=(3x+2)(x-4)$ .

Flashcard 8: What are the zeros of $f(x)=-(x-1)(x+6)$ ?

Answer: $x=1,-6$ . The negative sign doesn't affect the zeros, only the function's orientation.

Flashcard 9: What is the factored form of $2x^2+7x+3$ ?

Answer: $(2x+1)(x+3)$ . Use AC method: $2 \cdot 3 = 6$ , factors $1$ and $6$ add to $7$ .

Flashcard 10: What is the factored form of $x^2-16$ ?

Answer: $(x-4)(x+4)$ . Difference of squares: $x^2-16=(x-4)(x+4)$ .

Flashcard 11: What are the zeros of $f(x)=(x+3)(x+8)$ ?

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

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

Answer: $(x-2)(x-3)$ . Find two numbers that multiply to $6$ and add to $-5$ : $-2$ and $-3$ .

Flashcard 13: What is the factored form of $x^2-9x+20$ ?

Answer: $(x-4)(x-5)$ . Find two numbers that multiply to $20$ and add to $-9$ : $-4$ and $-5$ .

Flashcard 14: What is the factored form of $3x^2-12x$ ?

Answer: $3x(x-4)$ . Factor out the GCF of $3x$ .

Flashcard 15: What is the factored form of $x^2+13x+36$ ?

Answer: $(x+4)(x+9)$ . Find two numbers that multiply to $36$ and add to $13$ : $4$ and $9$ .

Flashcard 16: What is the factored form of $x^2+11x+24$ ?

Answer: $(x+3)(x+8)$ . Find two numbers that multiply to $24$ and add to $11$ : $3$ and $8$ .

Flashcard 17: What are the zeros of $f(x)=(3x+2)(x+3)$ ?

Answer: $x=-\frac{2}{3},-3$ . Set each factor equal to zero: $3x+2=0$ or $x+3=0$ .

Flashcard 18: What are the zeros of $f(x)=x^2-5x+6$ ?

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

Flashcard 19: What are the zeros of $f(x)=x^2-16$ ?

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

Flashcard 20: What is the factored form of $2x^2-5x-3$ ?

Answer: $(2x+1)(x-3)$ . Use AC method: $2 \cdot (-3) = -6$ , factors $-6$ and $1$ add to $-5$ .

Flashcard 21: What is the factored form of $x^2-8x+7$ ?

Answer: $(x-1)(x-7)$ . Find two numbers that multiply to $7$ and add to $-8$ : $-1$ and $-7$ .

Flashcard 22: What are the zeros of $f(x)=2x(x+5)$ ?

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

Flashcard 23: What are the zeros of $f(x)=3x(x-4)$ ?

Answer: $x=0,4$ . Set each factor equal to zero: $3x=0$ or $x-4=0$ .

Flashcard 24: What are the zeros of $f(x)=x^2-8x+7$ ?

Answer: $x=1,7$ . From factored form $x^2-8x+7=(x-1)(x-7)$ .

Flashcard 25: What is the factored form of $x^2-11x+24$ ?

Answer: $(x-3)(x-8)$ . Find two numbers that multiply to $24$ and add to $-11$ : $-3$ and $-8$ .

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

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

Flashcard 27: What are the zeros of $f(x)=x^2-9$ ?

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

Flashcard 28: What is the factored form of $x^2-13x+36$ ?

Answer: $(x-4)(x-9)$ . Find two numbers that multiply to $36$ and add to $-13$ : $-4$ and $-9$ .

Flashcard 29: What is the factored form of $3x^2+11x+6$ ?

Answer: $(3x+2)(x+3)$ . Use AC method: $3 \cdot 6 = 18$ , factors $2$ and $9$ add to $11$ .

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

Answer: $x=3$ with multiplicity $2$ . A repeated factor gives a zero with multiplicity equal to the exponent.

Flashcard 31: What are the zeros of $f(x)=(x+3)^2$ ?

Answer: $x=-3$ (double root). From $(x+3)^2=0$ , we get $x=-3$ with multiplicity $2$ .

Flashcard 32: What are the zeros of $f(x)=(x-4)(x-5)$ ?

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

Flashcard 33: What is the factored form of $x^2-9$ ?

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

Flashcard 34: What is the factored form of $x^2-3x-10$ ?

Answer: $(x-5)(x+2)$ . Find two numbers that multiply to $-10$ and add to $-3$ : $-5$ and $2$ .

Flashcard 35: What is the factored form of $x^2+6x+9$ ?

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

Flashcard 36: What are the zeros of $f(x)=(x+5)(x-3)$ ?

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

Flashcard 37: What is the standard factored form of a quadratic with zeros $r$ and $s$ and leading coefficient $a$ ?

Answer: $a(x-r)(x-s)$ . General form where $a$ is the leading coefficient and $r,s$ are zeros.

Flashcard 38: What is the factored form of $x^2-2x-8$ ?

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

Flashcard 39: What is the factored form of $x^2+2x-15$ ?

Answer: $(x+5)(x-3)$ . Find two numbers that multiply to $-15$ and add to $2$ : $5$ and $-3$ .

Flashcard 40: What are the zeros of $f(x)=(2x+1)(x+3)$ ?

Answer: $x=-\frac{1}{2},-3$ . Set each factor equal to zero: $2x+1=0$ or $x+3=0$ .

Flashcard 41: What is the factored form of $x^2+4x-21$ ?

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

Flashcard 42: What are the zeros of $f(x)=x^2-11x+24$ ?

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

Flashcard 43: What are the zeros of $f(x)=(x-7)(x+3)$ ?

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

Flashcard 44: What is the factored form of $4x^2-25$ ?

Answer: $(2x-5)(2x+5)$ . Difference of squares: $(2x)^2-5^2=(2x-5)(2x+5)$ .

Flashcard 45: What is the factored form of $2x^2+10x$ ?

Answer: $2x(x+5)$ . Factor out the GCF of $2x$ .

Flashcard 46: What is the factored form of $x^2+8x+7$ ?

Answer: $(x+1)(x+7)$ . Find two numbers that multiply to $7$ and add to $8$ : $1$ and $7$ .

Flashcard 47: What are the zeros of $f(x)=4x^2-25$ ?

Answer: $x=\frac{5}{2},-\frac{5}{2}$ . Set each factor equal to zero: $2x-5=0$ or $2x+5=0$ .

Flashcard 48: What is the factored form of $3x^2-10x-8$ ?

Answer: $(3x+2)(x-4)$ . Use AC method: $3 \cdot (-8) = -24$ , factors $2$ and $-12$ add to $-10$ .

Flashcard 49: What is the factored form of $x^2+9x+20$ ?

Answer: $(x+4)(x+5)$ . Find two numbers that multiply to $20$ and add to $9$ : $4$ and $5$ .

Flashcard 50: What is the factored form of $x^2+x-12$ ?

Answer: $(x+4)(x-3)$ . Find two numbers that multiply to $-12$ and add to $1$ : $4$ and $-3$ .

Algebra 2 Flashcards: Factor Quadratics To Find Zeros

Factor Quadratics To Find Zeros

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: What are the zeros of f(x)=x2−13x+36f(x)=x^2-13x+36f(x)=x2−13x+36?

Flashcard 2: 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)?

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

Flashcard 4: What are the zeros of f(x)=2x2−5x−3f(x)=2x^2-5x-3f(x)=2x2−5x−3?

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

Flashcard 6: What is the factored form of x2+7x+12x^2+7x+12x2+7x+12?

Flashcard 7: What are the zeros of f(x)=3x2−10x−8f(x)=3x^2-10x-8f(x)=3x2−10x−8?

Flashcard 8: What are the zeros of f(x)=−(x−1)(x+6)f(x)=-(x-1)(x+6)f(x)=−(x−1)(x+6)?

Flashcard 9: What is the factored form of 2x2+7x+32x^2+7x+32x2+7x+3?

Flashcard 10: What is the factored form of x2−16x^2-16x2−16?

Flashcard 11: What are the zeros of f(x)=(x+3)(x+8)f(x)=(x+3)(x+8)f(x)=(x+3)(x+8)?

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

Flashcard 13: What is the factored form of x2−9x+20x^2-9x+20x2−9x+20?

Flashcard 14: What is the factored form of 3x2−12x3x^2-12x3x2−12x?

Flashcard 15: What is the factored form of x2+13x+36x^2+13x+36x2+13x+36?

Flashcard 16: What is the factored form of x2+11x+24x^2+11x+24x2+11x+24?

Flashcard 17: What are the zeros of f(x)=(3x+2)(x+3)f(x)=(3x+2)(x+3)f(x)=(3x+2)(x+3)?

Flashcard 18: What are the zeros of f(x)=x2−5x+6f(x)=x^2-5x+6f(x)=x2−5x+6?

Flashcard 19: What are the zeros of f(x)=x2−16f(x)=x^2-16f(x)=x2−16?

Flashcard 20: What is the factored form of 2x2−5x−32x^2-5x-32x2−5x−3?

Flashcard 21: What is the factored form of x2−8x+7x^2-8x+7x2−8x+7?

Flashcard 22: What are the zeros of f(x)=2x(x+5)f(x)=2x(x+5)f(x)=2x(x+5)?

Flashcard 23: What are the zeros of f(x)=3x(x−4)f(x)=3x(x-4)f(x)=3x(x−4)?

Flashcard 24: What are the zeros of f(x)=x2−8x+7f(x)=x^2-8x+7f(x)=x2−8x+7?

Flashcard 25: What is the factored form of x2−11x+24x^2-11x+24x2−11x+24?

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

Flashcard 27: What are the zeros of f(x)=x2−9f(x)=x^2-9f(x)=x2−9?

Flashcard 28: What is the factored form of x2−13x+36x^2-13x+36x2−13x+36?

Flashcard 29: What is the factored form of 3x2+11x+63x^2+11x+63x2+11x+6?

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

Flashcard 31: What are the zeros of f(x)=(x+3)2f(x)=(x+3)^2f(x)=(x+3)2?

Flashcard 32: What are the zeros of f(x)=(x−4)(x−5)f(x)=(x-4)(x-5)f(x)=(x−4)(x−5)?

Flashcard 33: What is the factored form of x2−9x^2-9x2−9?

Flashcard 34: What is the factored form of x2−3x−10x^2-3x-10x2−3x−10?

Flashcard 35: What is the factored form of x2+6x+9x^2+6x+9x2+6x+9?

Flashcard 36: What are the zeros of f(x)=(x+5)(x−3)f(x)=(x+5)(x-3)f(x)=(x+5)(x−3)?

Flashcard 37: What is the standard factored form of a quadratic with zeros rrr and sss and leading coefficient aaa?

Flashcard 38: What is the factored form of x2−2x−8x^2-2x-8x2−2x−8?

Flashcard 39: What is the factored form of x2+2x−15x^2+2x-15x2+2x−15?

Flashcard 40: What are the zeros of f(x)=(2x+1)(x+3)f(x)=(2x+1)(x+3)f(x)=(2x+1)(x+3)?

Flashcard 41: What is the factored form of x2+4x−21x^2+4x-21x2+4x−21?

Flashcard 42: What are the zeros of f(x)=x2−11x+24f(x)=x^2-11x+24f(x)=x2−11x+24?

Flashcard 43: What are the zeros of f(x)=(x−7)(x+3)f(x)=(x-7)(x+3)f(x)=(x−7)(x+3)?

Flashcard 44: What is the factored form of 4x2−254x^2-254x2−25?

Flashcard 45: What is the factored form of 2x2+10x2x^2+10x2x2+10x?

Flashcard 46: What is the factored form of x2+8x+7x^2+8x+7x2+8x+7?

Flashcard 47: What are the zeros of f(x)=4x2−25f(x)=4x^2-25f(x)=4x2−25?

Flashcard 48: What is the factored form of 3x2−10x−83x^2-10x-83x2−10x−8?

Flashcard 49: What is the factored form of x2+9x+20x^2+9x+20x2+9x+20?

Flashcard 50: What is the factored form of x2+x−12x^2+x-12x2+x−12?