By LearningExpress Editors

Updated on Aug 24, 2011

To review these concepts, go to Factoring Polynomials Study Guide.

### Practice

Factor using the greatest common factor method.

- 5
*x*+ 25 - 100
*a*+ 300 - 15
*a*^{2}*b*^{2}+ 15*a**b*^{2} - 22
*x**y*+ 11*x* - 5
*x*+ 9 - 16
*x*^{2}+ 20*x* *x*^{2}*y*+ 3*x*- 8
*x*^{3}– 2*x*^{2}+ 4*x* - –6
*x*^{3}+ 18*x*^{2}*y* - 10
*x*^{4}*y*^{2}– 50*x*^{3}*y*+ 70 - 6
*a*^{2}– 39*a**b* - 12
*a*^{3}*b*^{2}*c*+ 4*a*^{5}*b**c*^{2} - 22
*x*^{4}*y*+ 55*x*^{2}*y*^{2} - 8
*x*^{2}+ 12*x*+ 20 - 5
*f*^{3}– 15*f*+ 25 - 30
*a*^{3}*b*^{2}+ 20*a*^{2}*b*+ 35*a*^{4}*b*^{2}

Factor using the difference of two squares method.

- 16
*r*^{2}– 121 *a*^{2}– 9*x*^{2}*y*^{2}– 49*b*^{2}– 100*r*^{2}–*s*^{2}- 36
*b*^{2}– 100 *a*^{6}–*b*^{6}*y*^{2}– 64- 4
*x*^{2}– 1 - 25
*x*^{2}– 4*y*^{2} *x*^{25}– 1*x*^{4}– 16*b*^{10}– 36- 16
*a*^{2}– 25*b*^{2}

Factor using the trinomial method.

*x*^{2}+ 9*x*+ 18*x*^{2}+ 6*x*+ 8*x*^{2}– 4*x*+ 3*x*^{2}+ 7*x*+ 12*x*^{2}– 10*x*+ 16*x*^{2}– 15*x*+ 14*x*^{2}+ 9*x*+ 20*x*^{2}– 12*x*+ 20*x*^{2}– 9*x*+ 20*x*^{2}– 11*x*+ 30

Factor the trinomials.

*a*^{2}–*a*– 20*r*^{2}– 7*r*– 18*x*^{2}– 6*x*– 7*x*^{2}+ 3*x*– 10*x*^{2}– 3*x*– 10*x*^{2}– 7*x*– 8*x*^{2}+ 6*x*– 16*x*^{2}– 4*x*– 21*x*^{2}+*x*– 30*x*^{2}– 3*x*– 18

### Solutions

- 5(
*x*+ 5) - 100(
*a*+ 3) - 15
*ab*(*ab*+*b*) - 11
*x*(2*y*+ 1) - prime—can't be factored
- 4
*x*(4*x*+ 5) *x*(*xy*+ 3)- 2
*x*(4*x*^{2}–*x*+ 2) - – 6
*x*^{2}(*x*– 3*y*), or 6*x*^{2}(–*x*+ 3*y*) - 10(
*x*^{4}*y*^{2}– 5*x*^{3}*y*+ 7) - 3
*a*(2*a*– 13*b*) - 4
*a*^{3}*bc*(3*b*+*a*^{2}*c*) - 11
*x*^{2}*y*(2*x*^{2}+ 5*y*) - 4(2
*x*^{2}+ 3*x*+ 5) - 5(
*f*3 – 3*f*+ 5) - 5
*a*^{2}*b*(6*ab*+ 4 + 7*a*^{2}*b*) - (4
*r*+ 11)(4*r*– 11) - (
*a*+ 3)(*a*– 3) - (
*xy*+ 7)(*xy*– 7) - (
*b*+ 10)(*b*– 10) - (
*r*+*s*)(*r*&38211;*s*) - (6
*b*+ 10)(6*b*– 10) - (
*a*^{3}+*b*^{3})(*a*^{3}–*b*^{3}) - (
*y*+ 8)(*y*– 8) - (2
*x*+ 1)(2*x*– 1) - (5
*x*+ 2*y*)(5*x*– 2*y*) - prime—can't be factored (because
*x*^{25}is not a perfect square) - (
*x*^{2}+ 4)(*x*^{2}– 4) - (
*b*^{5}– 6)(*b*^{5}+ 6) - (4
*a*– 5*b*)(4*a*+ 5*b*) - (
*x*+ 3)(*x*+ 6) - (
*x*+ 4)(*x*+ 2) - (
*x*– 1)(*x*– 3) - (
*x*+ 4)(*x*+ 3) - (
*x*– 8)(*x*– 2) - (
*x*– 14)(*x*– 1) - (
*x*+ 5)(*x*+ 4) - (
*x*– 10)(*x*– 2) - (
*x*– 4)(*x*– 5) - (
*x*– 6)(*x*– 5) - (
*a*+ 4)(*a*– 5) - (
*r*– 9)(*r*+ 2) - (
*x*+ 1)(*x*– 7) - (
*x*+ 5)(*x*– 2) - (
*x*– 5)(*x*+ 2) - (
*x*– 8)(*x*+ 1) - (
*x*+ 8)(*x*– 2) - (
*x*– 7)(*x*+ 3) - (
*x*+ 6)(*x*– 5) - (
*x*– 6)(*x*+ 3)

From Algebra Success in 20 Minutues A Day. Copyright © 2008 by LearningExpress, LLC. All Rights Reserved.

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