This leads to the completely factored form.

CHECK

FOIL; Combine like terms.

= 15 y^3 + 55 y^2 + 30 y ✓ Distributive property

= 5 y 13 y^2 + 11 y+ 62

5 y 13 y+ 221 y+ 32

= 5 y 13 y+ 221 y+ 32

15 y^3 + 55 y^2 + 30 y

378 CHAPTER 6 Factoring and Applications

Remember the

common factor.

(b)

The common factor could be 3aor If we factor out the first term of

the trinomial will be positive, which makes it easier to factor the remaining trinomial.

Factor out.

Factor the trinomial.

Checkby multiplying. NOW TRY

=- 3 a 14 a- 3212 a+ 52

= - 3 a 18 a^2 + 14 a- 152 - 3 a

- 24 a^3 - 42 a^2 + 45 a

- 3 a. - 3 a,

- 24 a^3 - 42 a^2 + 45 a

CAUTION Include the common factor in the final factored form.

Complete solution available
on the Video Resources on DVD

6.3 EXERCISES

Concept Check The middle term of each trinomial has been rewritten. Now factor by

grouping.

NOW TRY
EXERCISE 7
Factor .- 10 x^3 - 45 x^2 + 90 x

NOW TRY ANSWER

7. 
   
   
   
   • 5 x 12 x- 321 x+ 62
   
   
   
   

1. 2.

= 6 x^2 + 9 x+ 4 x+ 6

6 x^2 + 13 x+ 6

= 10 t^2 + 5 t+ 4 t+ 2

10 t^2 + 9 t+ 2

3. 4.

= 12 p^2 - 9 p- 8 p+ 6

12 p^2 - 17 p+ 6

= 15 z^2 - 10 z- 9 z+ 6

15 z^2 - 19 z+ 6

5. 6.

= 3 x^2 - 7 xy+ 6 xy- 14 y^2

3 x^2 - xy- 14 y^2

= 8 s 2 - 4 st+ 6 st- 3 t^2

8 s^2 + 2 st- 3 t^2

Concept Check Complete the steps to factor each trinomial by grouping.

7.

(a)Find two integers whose product is

and whose sum is.

(b)The required integers are

and.

(c)Write the middle term, 11m, as

.

(d)Rewrite the given trinomial as

.

(e)Factor the polynomial in part (d)

by grouping.

(f )Check by multiplying.

8.

(a)Find two integers whose product is

and whose sum is.

(b)The required integers are

and.

(c)Write the middle term, as

.

(d)Rewrite the given trinomial as

.

(e)Factor the polynomial in part (d)

by grouping.

(f )Check by multiplying.

+

• 19 y,

=

6 y^2 - 19 y+ 10

+

=

2 m^2 + 11 m+ 12

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