Algebra 1 A.2 Factoring Quiz STUDY GUIDE
Mrs. Grieser
Name: _____________________________ Date: _______________ Block: _________
SOL A.2 Factoring QUIZ STUDY GUIDE
Textbook Sections: 9.4, 9.5, 9.7
Know how to…

Factor polynomials by factoring out greatest common factor (GCF) (type I
factoring)
o Example: 4x2 + 2x = 2x(2x + 1)
o Always factor out GCF prior to any other factoring!
o Sometimes the GCF is -1; don’t forget to factor it out first
o Example: Factor –x4 + 3


–x4 + 3 = -(x4 – 3)
Factor polynomials by recognizing the sum and difference pattern (type II)
o Example: 25x2 – 16 = (5x – 4)(5x + 4)

Factor polynomials of the form x2 + bx + c (type III)
o Example: x2 + 5x + 6 = (x + 3)(x + 2)

After factoring, always verify solutions by multiplying factors to get original
polynomial

Solve equations by factoring first and using the zero product property
o Example: Solve x2 - 11x + 28 = 0


Factor first: (x - 4)(x – 7) = 0

Use zero product property: x – 4 = 0 when x = 4; x – 7 = 0 when x = 7
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Solutions: x = 4, 7
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Verify solutions by plugging back into the original polynomial and/or
graphing!
Find zeros (or roots) of a function
o Example: Find the zeros of f(x) = x2 + 2x – 24

Zeros are the x-intercepts of a function and occur when f(x) = 0

Set f(x) = 0 and solve

x2 + 2x – 24 = 0

(x + 6)(x – 4) = 0
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zeros occur at x = -6 and x = 4
Algebra 1 A.2 Factoring Quiz STUDY GUIDE
Mrs. Grieser
Study questions:
1)
2)
Factor the polynomials.
a) 15x2 + 5xy
b) 12x2 – 24x3
c) 11x – 22x2
d) -5x4 – 20x2
e) x2 – 121
f) 81x2 – 100y2
g) 10x2 – 10y2
h) x2 + 12x + 20
i) x2 – 9x + 14
j) x2 – 2x – 35
k) 2x2 – 2x - 84
l) –x2 + 9x – 18
Find the solution(s) to the equations.
a) (x – 4)(x + 5) = 0
b) x3 – 100x = 0
d) x2 –15x + 36 = 0
e) x2 – 4x = 21
3) Find the zeros (roots) of the functions.
a) f(x) = -3x2 – 6x
b) g(x) = 8x2 – 16x
d) f(x) = -x2 + x + 20
e) f(x) = 2x2 – 8x + 6
c) 90 – 10x2 = 0
f) x2 – 9x + 25 = 5
c) h(x) = x2 – 10x + 16
f) f(x) = -2x2 - 6x + 36
Algebra 1 A.2 Factoring Quiz STUDY GUIDE
Mrs. Grieser
STUDY QUESTION ANSWERS
1a) 5x(3x + y)
1b) 12x2(1 – 2x)
1c) 11x(1 – 2x)
1d) -5x2(x2 + 4)
1e) (x + 11)(x – 11)
1f) (9x + 10y)(9x – 10y)
1g) 10(x + y)(x – y)
1h) (x + 10)(x + 2)
1i) (x – 7)(x – 2)
1j) (x – 7)(x + 5)
1k) 2(x – 7)(x + 6)
1l) –(x – 6)(x – 3)
2a) x = -5, 4
2b) x(x + 10)(x – 10) = 0; x = 0, 10, -10
2c) 10(3 + x)(3 – x) =0; x = -3, 3
2d) (x – 12)(x – 3) = 0; x = 3, 12
2e) (x + 3)(x – 7) = 0; x = -3, 7
2f) (x – 5)(x – 4) = 0; x = 4, 5
3a) x = 0, -2
3b) x = 0, 2
3c) x = 2, 8
3d) x = -4, 5
3e) x = 1, 3
3f) x = -6, 3