56. 57. 58.
59. 60.
61. 62.
Brain Busters Factor each polynomial.
- 13 m-n 2 k^2 - 1313 m-n 2 k+ 4013 m-n 2
12 p+q 2 r^2 - 1212 p+q 2 r+ 2712 p+q 21 x+y 2 n^2 + 1 x+y 2 n- 201 x+y 21 a+b 2 x^2 + 1 a+b 2 x- 121 a+b 2k^7 - 2 k^6 m- 15 k^5 m^2 z^10 - 4 z^9 y- 21 z^8 y^2 x^9 + 5 x^8 w- 24 x^7 w^2a^5 + 3 a^4 b- 4 a^3 b^2 m^3 n- 2 m^2 n^2 - 3 mn^3 y^3 z+y^2 z^2 - 6 yz^3m^3 n- 10 m^2 n^2 + 24 mn^3 y^3 z+ 3 y^2 z^2 - 54 yz^35 m^5 + 25 m^4 - 40 m^212 k^5 - 6 k^3 + 10 k^23 t^3 + 27 t^2 + 24 t 2 x^6 + 8 x^5 - 42 x^44 y^5 + 12 y^4 - 40 y^3SECTION 6.3 More on Factoring Trinomials 373
Find each product. See Section 5.5.- 12 y- 721 y+ 42 74. 13 a+ 2212 a+ 12 75. 15 z+ 2213 z- 22
PREVIEW EXERCISES
OBJECTIVES
More on Factoring Trinomials
6.3
1 Factor trinomials by
grouping when the
coefficient of the
second-degree term
is not 1.
2 Factor trinomials
by using the FOIL
method.
Trinomials such as in which the coefficient of the second-degree term
is not1, are factored with extensions of the methods from the previous sections.
OBJECTIVE 1 Factor trinomials by grouping when the coefficient of the
second-degree term is not 1. A trinomial such as is factored by
finding two numbers whose product is 2 and whose sum is 3. To factor
we look for two integers whose product is and whose sum is 7.
Sum is 7.Product is.By considering pairs of positive integers whose product is 12, we find the required inte-
gers, 3 and 4. We use these integers to write the middle term, 7x, as
7 x
Group the terms.
Factor each group.Must be the same factor
Factor out 2x + 3.CHECK Multiply to obtain 12 x+ 321 x+ 22 2 x^2 + 7 x+6. ✓
= 12 x+ 321 x+ 22
=x 12 x+ 32 + 212 x+ 32
= 12 x^2 + 3 x 2 + 14 x+ 62
= 2 x^2 + 3 x+ 4 x+ 6
2 x^2 + 7 x+ 6
7 x= 3 x+ 4 x.
2 # 6 = 12
2 x^2 + 7 x+ 6
2 # 6 = 12