Algebra Flashcards: Factor Quadratics To Find Zeros

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

Algebra

Factor Quadratics To Find Zeros

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QUESTION

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What are the zeros of $f(x)$ if $f(x)=(x-1)(x-9)$ ?

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ANSWER

$x=1$ and $x=9$ . Set each factor equal to zero: $(x-1)=0$ and $(x-9)=0$ .

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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.

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 $f(x)$ if $f(x)=(x-1)(x-9)$ ?

Answer: $x=1$ and $x=9$ . Set each factor equal to zero: $(x-1)=0$ and $(x-9)=0$ .

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

Answer: $x=4$ and $x=-4$ . From $(x-4)(x+4)=0$ , set each factor to zero.

Flashcard 3: What are the zeros of $f(x)=x^2-9x+20$ after factoring?

Answer: $x=5$ and $x=4$ . From $(x-5)(x-4)=0$ , set each factor to zero.

Flashcard 4: What is the first step to factor $6x^2+9x$ to reveal zeros?

Answer: Factor out the GCF: $3x(2x+3)$ . Factor out the greatest common factor before finding zeros.

Flashcard 5: What is the factored form of $x^2-5x-14$ ?

Answer: $(x-7)(x+2)$ . Find two numbers that multiply to $-14$ and add to $-5$ : $-7$ and 2.

Flashcard 6: What is the factored form of $4x^2-12x+9$ ?

Answer: $(2x-3)^2$ . Perfect square trinomial: $(2x-3)^2$ .

Flashcard 7: What are the zeros of $f(x)=x^2+12x+35$ after factoring?

Answer: $x=-5$ and $x=-7$ . From $(x+5)(x+7)=0$ , set each factor to zero.

Flashcard 8: What are the zeros of $f(x)=x^2-12x+35$ after factoring?

Answer: $x=5$ and $x=7$ . From $(x-5)(x-7)=0$ , set each factor to zero.

Flashcard 9: 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 $-3$ .

Flashcard 10: What are the zeros of $f(x)=x^2+12x+35$ after factoring?

Answer: $x=-5$ and $x=-7$ . From $(x+5)(x+7)=0$ , set each factor to zero.

Flashcard 11: What is the factored form of $x^2-9x+20$ ?

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

Flashcard 12: What are the zeros of $f(x)=x^2+7x+12$ after factoring?

Answer: $x=-3$ and $x=-4$ . From $(x+3)(x+4)=0$ , set each factor to zero.

Flashcard 13: What are the zeros of $f(x)$ if $f(x)=(2x+3)^2$ ?

Answer: $x=-\frac{3}{2}$ (double root). Square factor gives one zero with multiplicity 2.

Flashcard 14: What is the factored form of $x^2+5x-14$ ?

Answer: $(x+7)(x-2)$ . Find two numbers that multiply to $-14$ and add to 5: 7 and $-2$ .

Flashcard 15: What is the factored form of $x^2-6x$ ?

Answer: $x(x-6)$ . Factor out GCF of $x$ from both terms.

Flashcard 16: What is the factored form of $x^2-12x+35$ ?

Answer: $(x-5)(x-7)$ . Find two numbers that multiply to 35 and add to $-12$ : $-5$ and $-7$ .

Flashcard 17: What are the zeros of $f(x)=x^2+3x-10$ after factoring?

Answer: $x=-5$ and $x=2$ . From $(x+5)(x-2)=0$ , set each factor to zero.

Flashcard 18: What are the zeros of $f(x)$ if $f(x)=(3x+6)(x-5)$ ?

Answer: $x=-2$ and $x=5$ . Set each factor equal to zero: $(3x+6)=0$ gives $x=-2$ .

Flashcard 19: 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 20: What is the factored form of $2x^2+5x+3$ ?

Answer: $(2x+3)(x+1)$ . Use AC method or trial factoring with leading coefficient 2.

Flashcard 21: What are the zeros of $f(x)=2x^2+8x$ using its factored form?

Answer: $x=0$ and $x=-4$ . From $2x(x+4)=0$ , set each factor to zero.

Flashcard 22: What are the zeros of $f(x)$ if $f(x)=(5x-10)(2x+1)$ ?

Answer: $x=2$ and $x=-\frac{1}{2}$ . Set each factor equal to zero: $(5x-10)=0$ gives $x=2$ .

Flashcard 23: What are the zeros of $f(x)=3x^2-12$ using the factored form?

Answer: $x=2$ and $x=-2$ . From $3(x-2)(x+2)=0$ , only the linear factors give zeros.

Flashcard 24: What are the zeros of $f(x)=x^2-6x$ after factoring?

Answer: $x=0$ and $x=6$ . From $x(x-6)=0$ , set each factor to zero.

Flashcard 25: What is the factored form of $x^2+12x+35$ ?

Answer: $(x+5)(x+7)$ . Find two numbers that multiply to 35 and add to 12: 5 and 7.

Flashcard 26: 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 $-3$ .

Flashcard 27: What is the factored form of $x^2-25$ ?

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

Flashcard 28: What are the zeros of $f(x)=3x^2+2x-8$ after factoring?

Answer: $x=\frac{4}{3}$ and $x=-2$ . From $(3x-4)(x+2)=0$ , set each factor to zero.

Flashcard 29: What is the factored form of $2x^2+8x$ ?

Answer: $2x(x+4)$ . Factor out GCF of $2x$ from both terms.

Flashcard 30: What are the zeros of $f(x)=2x^2+5x+3$ after factoring?

Answer: $x=-\frac{3}{2}$ and $x=-1$ . From $(2x+3)(x+1)=0$ , set each factor to zero.

Flashcard 31: 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 32: What are the zeros of $f(x)$ if $f(x)=(4x-3)(x-2)$ ?

Answer: $x=\frac{3}{4}$ and $x=2$ . Set each factor equal to zero: $(4x-3)=0$ gives $x=\frac{3}{4}$ .

Flashcard 33: What is the factored form of $3x^2-12$ ?

Answer: $3(x-2)(x+2)$ . Factor out 3, then use difference of squares.

Flashcard 34: What are the zeros of $f(x)$ if $f(x)=(x-4)^2$ ?

Answer: $x=4$ (double root). Square factor gives one zero with multiplicity 2.

Flashcard 35: 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 36: What is the factored form of $x^2-9x+20$ ?

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

Flashcard 37: What is the factored form of $x^2+10x+25$ ?

Answer: $(x+5)^2$ . Perfect square trinomial: $a^2+2ab+b^2=(a+b)^2$ .

Flashcard 38: What are the zeros of $f(x)=2x^2-x-3$ after factoring?

Answer: $x=\frac{3}{2}$ and $x=-1$ . From $(2x-3)(x+1)=0$ , set each factor to zero.

Flashcard 39: What is the factored form of $2x^2+5x+3$ ?

Answer: $(2x+3)(x+1)$ . Use AC method or trial factoring with leading coefficient 2.

Flashcard 40: What are the zeros of $f(x)=x^2-9x+20$ after factoring?

Answer: $x=5$ and $x=4$ . From $(x-5)(x-4)=0$ , set each factor to zero.

Flashcard 41: 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 42: What property connects factors to zeros in $f(x)=a(x-r_1)(x-r_2)$ ?

Answer: Zero product property: $f(x)=0\Rightarrow x=r_1$ or $x=r_2$ . If a product equals zero, at least one factor must be zero.

Flashcard 43: 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 44: What are the zeros of $f(x)=x^2+5x-14$ after factoring?

Answer: $x=-7$ and $x=2$ . From $(x+7)(x-2)=0$ , set each factor to zero.

Flashcard 45: What are the zeros of $f(x)=x^2+10x+25$ after factoring?

Answer: $x=-5$ (double root). From $(x+5)^2=0$ , the repeated factor gives one zero.

Flashcard 46: What is the factored form of $2x^2-x-3$ ?

Answer: $(2x-3)(x+1)$ . Use AC method or trial factoring with leading coefficient 2.

Flashcard 47: What is the factored form of $x^2+2x-24$ ?

Answer: $(x+6)(x-4)$ . Find two numbers that multiply to $-24$ and add to 2: 6 and $-4$ .

Flashcard 48: What is the factored form of $x^2-13x+36$ ?

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

Flashcard 49: What is the factored form of $3x^2+2x-8$ ?

Answer: $(3x-4)(x+2)$ . Use AC method or trial factoring with leading coefficient 3.

Flashcard 50: What are the zeros of $f(x)=x^2-5x-14$ after factoring?

Answer: $x=7$ and $x=-2$ . From $(x-7)(x+2)=0$ , set each factor to zero.

Flashcard 51: What is the factored form of $x^2-16$ ?

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

Flashcard 52: What is the factored form of $x^2-25$ ?

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

Flashcard 53: What is the factored form of $x^2-13x+36$ ?

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

Flashcard 54: What are the zeros of $f(x)$ if $f(x)=(x+8)(x+1)$ ?

Answer: $x=-8$ and $x=-1$ . Set each factor equal to zero: $(x+8)=0$ and $(x+1)=0$ .

Flashcard 55: What are the zeros of $f(x)=3x(2x+3)$ ?

Answer: $x=0$ and $x=-\frac{3}{2}$ . Set each factor to zero: $3x=0$ and $(2x+3)=0$ .

Algebra 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)f(x)f(x) if f(x)=(x−1)(x−9)f(x)=(x-1)(x-9)f(x)=(x−1)(x−9)?

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

Flashcard 3: What are the zeros of f(x)=x2−9x+20f(x)=x^2-9x+20f(x)=x2−9x+20 after factoring?

Flashcard 4: What is the first step to factor 6x2+9x6x^2+9x6x2+9x to reveal zeros?

Flashcard 5: What is the factored form of x2−5x−14x^2-5x-14x2−5x−14?

Flashcard 6: What is the factored form of 4x2−12x+94x^2-12x+94x2−12x+9?

Flashcard 7: What are the zeros of f(x)=x2+12x+35f(x)=x^2+12x+35f(x)=x2+12x+35 after factoring?

Flashcard 8: What are the zeros of f(x)=x2−12x+35f(x)=x^2-12x+35f(x)=x2−12x+35 after factoring?

Flashcard 9: What is the factored form of x2+x−12x^2+x-12x2+x−12?

Flashcard 10: What are the zeros of f(x)=x2+12x+35f(x)=x^2+12x+35f(x)=x2+12x+35 after factoring?

Flashcard 11: What is the factored form of x2−9x+20x^2-9x+20x2−9x+20?

Flashcard 12: What are the zeros of f(x)=x2+7x+12f(x)=x^2+7x+12f(x)=x2+7x+12 after factoring?

Flashcard 13: What are the zeros of f(x)f(x)f(x) if f(x)=(2x+3)2f(x)=(2x+3)^2f(x)=(2x+3)2?

Flashcard 14: What is the factored form of x2+5x−14x^2+5x-14x2+5x−14?

Flashcard 15: What is the factored form of x2−6xx^2-6xx2−6x?

Flashcard 16: What is the factored form of x2−12x+35x^2-12x+35x2−12x+35?

Flashcard 17: What are the zeros of f(x)=x2+3x−10f(x)=x^2+3x-10f(x)=x2+3x−10 after factoring?

Flashcard 18: What are the zeros of f(x)f(x)f(x) if f(x)=(3x+6)(x−5)f(x)=(3x+6)(x-5)f(x)=(3x+6)(x−5)?

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

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

Flashcard 21: What are the zeros of f(x)=2x2+8xf(x)=2x^2+8xf(x)=2x2+8x using its factored form?

Flashcard 22: What are the zeros of f(x)f(x)f(x) if f(x)=(5x−10)(2x+1)f(x)=(5x-10)(2x+1)f(x)=(5x−10)(2x+1)?

Flashcard 23: What are the zeros of f(x)=3x2−12f(x)=3x^2-12f(x)=3x2−12 using the factored form?

Flashcard 24: What are the zeros of f(x)=x2−6xf(x)=x^2-6xf(x)=x2−6x after factoring?

Flashcard 25: What is the factored form of x2+12x+35x^2+12x+35x2+12x+35?

Flashcard 26: What is the factored form of x2+x−12x^2+x-12x2+x−12?

Flashcard 27: What is the factored form of x2−25x^2-25x2−25?

Flashcard 28: What are the zeros of f(x)=3x2+2x−8f(x)=3x^2+2x-8f(x)=3x2+2x−8 after factoring?

Flashcard 29: What is the factored form of 2x2+8x2x^2+8x2x2+8x?

Flashcard 30: What are the zeros of f(x)=2x2+5x+3f(x)=2x^2+5x+3f(x)=2x2+5x+3 after factoring?

Flashcard 31: What is the factored form of x2−2x−15x^2-2x-15x2−2x−15?

Flashcard 32: What are the zeros of f(x)f(x)f(x) if f(x)=(4x−3)(x−2)f(x)=(4x-3)(x-2)f(x)=(4x−3)(x−2)?

Flashcard 33: What is the factored form of 3x2−123x^2-123x2−12?

Flashcard 34: What are the zeros of f(x)f(x)f(x) if f(x)=(x−4)2f(x)=(x-4)^2f(x)=(x−4)2?

Flashcard 35: What is the factored form of x2+7x+12x^2+7x+12x2+7x+12?

Flashcard 36: What is the factored form of x2−9x+20x^2-9x+20x2−9x+20?

Flashcard 37: What is the factored form of x2+10x+25x^2+10x+25x2+10x+25?

Flashcard 38: What are the zeros of f(x)=2x2−x−3f(x)=2x^2-x-3f(x)=2x2−x−3 after factoring?

Flashcard 39: What is the factored form of 2x2+5x+32x^2+5x+32x2+5x+3?

Flashcard 40: What are the zeros of f(x)=x2−9x+20f(x)=x^2-9x+20f(x)=x2−9x+20 after factoring?

Flashcard 41: What is the factored form of x2+7x+12x^2+7x+12x2+7x+12?

Flashcard 42: What property connects factors to zeros in f(x)=a(x−r1)(x−r2)f(x)=a(x-r_1)(x-r_2)f(x)=a(x−r1​)(x−r2​)?

Flashcard 43: What is the factored form of x2+3x−10x^2+3x-10x2+3x−10?

Flashcard 44: What are the zeros of f(x)=x2+5x−14f(x)=x^2+5x-14f(x)=x2+5x−14 after factoring?

Flashcard 45: What are the zeros of f(x)=x2+10x+25f(x)=x^2+10x+25f(x)=x2+10x+25 after factoring?

Flashcard 46: What is the factored form of 2x2−x−32x^2-x-32x2−x−3?

Flashcard 47: What is the factored form of x2+2x−24x^2+2x-24x2+2x−24?

Flashcard 48: What is the factored form of x2−13x+36x^2-13x+36x2−13x+36?

Flashcard 49: What is the factored form of 3x2+2x−83x^2+2x-83x2+2x−8?

Flashcard 50: What are the zeros of f(x)=x2−5x−14f(x)=x^2-5x-14f(x)=x2−5x−14 after factoring?

Flashcard 51: What is the factored form of x2−16x^2-16x2−16?

Flashcard 52: What is the factored form of x2−25x^2-25x2−25?

Flashcard 53: What is the factored form of x2−13x+36x^2-13x+36x2−13x+36?

Flashcard 54: What are the zeros of f(x)f(x)f(x) if f(x)=(x+8)(x+1)f(x)=(x+8)(x+1)f(x)=(x+8)(x+1)?

Flashcard 55: What are the zeros of f(x)=3x(2x+3)f(x)=3x(2x+3)f(x)=3x(2x+3)?