356 CHAPTER 6 Factoring
6.4 A General Approach to Factoring
Step 1 Factor out any common factors.
Step 2 For a binomial, check for the difference of
squares, the difference of cubes, or the sum of
cubes.
For a trinomial, see if it is a perfect square. If
not, factor as in Section 6.2.
For more than three terms, try factoring by
grouping.
Step 3 Check the factored form by multiplying.
Factor.
Factor out the
common factor.
Factor by grouping.
Factor the difference
of squares.
=a 1 k+ 221 k- 321 k+ 32
=a 31 k+ 221 k^2 - 924
=a 3 k^21 k+ 22 - 91 k+ 224
=a 31 k^3 + 2 k^22 - 19 k+ 1824
=a 1 k^3 + 2 k^2 - 9 k- 182
ak^3 + 2 ak^2 - 9 ak- 18 a
CONCEPTS EXAMPLES
6.5 Solving Equations by Factoring
Step 1 Rewrite the equation if necessary so that one
side is 0.
Step 2 Factor the polynomial.
Step 3 Set each factor equal to 0.
Step 4 Solve each equation from Step 3.
Step 5 Check each solution.
Solve.
Standard form
Factor.
or Zero-factor property
or
A check verifies that the solution set is E-3,^12 F.
x=
1
2
2 x= 1 x=- 3
2 x- 1 = 0 x+ 3 = 0
12 x- 121 x+ 32 = 0
2 x^2 + 5 x- 3 = 0
2 x^2 + 5 x= 3
REVIEW EXERCISES
CHAPTER 6
6.1 Factor out the greatest common factor.
1. 2.
3. 4.
5. 6.
Factor by grouping.
6.2 Factor completely.
11. 12. 13.
14. 15. 16.
17. 18.
19. 20.
21.p^21 p+ 222 +p 1 p+ 222 - 61 p+ 222 22. 31 r+ 522 - 111 r+ 52 - 4
y^4 + 2 y^2 - 8 2 k 4 - 5 k^2 - 3
24 x- 2 x^2 - 2 x^36 b^3 - 9 b^2 - 15 b
10 m^2 + 37 m+ 30 10 k^2 - 11 kh+ 3 h 2 9 x^2 + 4 xy- 2 y^2
3 p^2 - p- 4 6 k^2 + 11 k- 10 12 r^2 - 5 r- 3
2 m+ 6 - am- 3 a x^2 + 3 x- 3 y-xy
4 m+nq+mn+ 4 q x^2 + 5 y+ 5 x+xy
1 x+ 3214 x- 12 - 1 x+ 3213 x+ 22 1 z+ 121 z- 42 + 1 z+ 1212 z+ 32
12 q^2 b+ 8 qb^2 - 20 q^3 b^26 r^3 t- 30 r^2 t^2 + 18 rt^3
12 p^2 - 6 p 21 x^2 + 35 x