Intermediate Algebra (11th edition)

Rearranging Terms before Factoring by Grouping

Factor

Neither the first two terms nor the last two terms have a common factor except 1.

We can rearrange and group the terms as follows.

Rearrange and group the terms.

Factor out the common factors.

Factor out Use parentheses.

CHECK

FOIL

=p^2 q^2 - 10 - 2 q^2 + 5 p^2 ✓ Original polynomial

=p^2 q^2 + 5 p^2 - 2 q^2 - 10

1 p^2 - 221 q^2 + 52

= 1 p^2 - 221 q^2 + 52 p^2 - 2.

=q^21 p^2 - 22 + 51 p^2 - 22

= 1 p^2 q^2 - 2 q^22 + 15 p^2 - 102

p^2 q^2 - 10 - 2 q^2 + 5 p^2

p^2 q^2 - 10 - 2 q^2 + 5 p^2.

EXAMPLE 8

324 CHAPTER 6 Factoring

NOW TRY
EXERCISE 8
Factor.

2 kp^2 + 6 - 3 p^2 - 4 k

NOW TRY ANSWER

8. 1 p^2 - 2212 k- 32

Don’t stop here.

NOW TRY

CAUTION In Example 8,do not stop at the step

This expression is not in factored form,because it is a sumof two terms,

and not a 51 p^2 - 22 , product.

q^21 p^2 - 22

q^21 p^2 - 22 + 51 p^2 - 22.

Complete solution available
on the Video Resources on DVD

6.1 EXERCISES

Factor out the greatest common factor. Simplify the factors, if possible. See Examples 1– 4.

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    32.- 9 a^21 p+q 2 - 3 a^31 p+q 22 + 6 a 1 p+q 23

    
    

51 m+p 23 - 101 m+p 22 - 151 m+p 24

61 a+ 2 b 22 - 41 a+ 2 b 23 + 121 a+ 2 b 24

1512 z+ 123 + 1012 z+ 122 - 2512 z+ 12

413 - x 22 - 13 - x 23 + 313 - x 2 21 t-s 2 + 41 t-s 22 - 1 t-s 23

512 - x 22 - 212 - x 23 215 - x 23 - 315 - x 22

12 z- 121 z+ 62 - 12 z- 121 z- 52 13 x+ 221 x- 42 - 13 x+ 221 x+ 82

1 m- 421 m+ 22 + 1 m- 421 m+ 32 1 z- 521 z+ 72 + 1 z- 521 z+ 102

14 a^3 b^2 + 7 a^2 b- 21 a^5 b^3 + 42 ab^412 km^3 - 24 k^3 m^2 + 36 k^2 m^4 - 60 k^4 m^3

16 z^2 n^6 + 64 zn^7 - 32 z^3 n^35 r^3 s 5 + 10 r^2 s 2 - 15 r^4 s 2

15 a^2 c^3 - 25 ac^2 + 5 ac 15 y^3 z^3 - 27 y^2 z^4 + 3 yz^3

10 t^5 - 2 t^3 - 4 t^46 p^3 - 3 p^2 - 9 p^4

• 3 z^5 w 2 - 18 z^3 w 4 7 x^3 + 35 x 4 - 14 x^56 k^3 - 36 k^4 - 48 k^5

8 k^3 + 24 k 9 z^4 + 81 z - 4 p^3 q^4 - 2 p^2 q^5

9 + 27 x 8 y- 15 7 x- 40

12 m- 60 15 r- 45 4 + 20 z