6.Concept Check InExercise 5,what must be true of aand bif the coefficient of the con-
stant term is positive?
7.What is meant by a prime polynomial?
8.How can you check your work when factoring a trinomial? Does the check ensure that the
trinomial is completely factored?
9.Concept Check Which is the correct factored form of?
A. B.
C. D.
10.Concept Check What is the suggested first step in factoring? (See
Example 7.)
11.Concept Check What polynomial can be factored as?
12.Concept Check What polynomial can be factored as 1 y- 721 y+ 32?
1 a+ 921 a+ 42
2 x^3 + 8 x^2 - 10 x
1 x- 821 x- 42 1 x+ 821 x+ 42
1 x- 821 x+ 42 1 x+ 821 x- 42
x^2 - 12 x+ 32
372 CHAPTER 6 Factoring and Applications
13. 14.
= 1 x+ 721 2
x^2 + 10 x+ 21
= 1 p+ 521 2
p^2 + 11 p+ 30
15. 16.
= 1 r+ 721 2
r^2 + 15 r+ 56
= 1 x+ 421 2
x^2 + 15 x+ 44
17. 18.
= 1 t- 221 2
t^2 - 14 t+ 24
= 1 x- 121 2
x^2 - 9 x+ 8
19. 20.
= 1 t+ 621 2
t^2 - t- 42
= 1 y+ 321 2
y^2 - 2 y- 15
21. 22.
= 1 x- 321 2
x^2 + 6 x- 27
= 1 x- 221 2
x^2 + 9 x- 22
23. 24.
= 1 y+ 421 2
y^2 - 2 y- 24
= 1 y+ 221 2
y^2 - 7 y- 18
Factor completely. If the polynomial cannot be factored, write prime. See Examples 1–5.
(Hint:In Exercises 43 and 44, first write the trinomial in descending powers and then factor.)
- 43.- 32 + 14 x+x^2 44.- 39 + 10 x+x^2
d^2 - 4 d- 45 x^2 + 3 x- 39 m^2 + 10 m- 30
r^2 - r- 30 q^2 - q- 42 a^2 - 8 a- 48
t^2 + 11 t+ 12 z^2 - 15 z+ 56 x^2 - 13 x+ 36
y^2 - 8 y+ 15 y^2 - 6 y+ 8 x^2 + 4 x+ 5
x^2 + 6 x+ 8 m^2 +m- 20 p^2 + 4 p- 5
y^2 + 9 y+ 8 a^2 + 9 a+ 20 b^2 + 8 b+ 15
Factor completely. See Example 6.
- 51.v^2 - 11 vw+ 30 w^2 52.v^2 - 11 vx+ 24 x^2
a^2 - ab- 12 b^2 x^2 + 4 xy+ 3 y^2 p^2 + 9 pq+ 8 q^2
r^2 + 3 ra+ 2 a^2 x^2 + 5 xa+ 4 a^2 t^2 - tz- 6 z^2
Factor completely. See Example 7.
- 4 x^2 + 12 x- 40 54. 5 y^2 - 5 y- 30 55. 2 t^3 + 8 t^2 + 6 t
Complete each factoring. See Examples 1– 4.
http://www.ebook777.com
http://www.ebook777.com
