Download 2 Factor when a and c Are not Prime Numbers 3 Factor with a

EXAMPLE
2
Factor when a and c Are not Prime Numbers
Factor 6x2 19x 15.
Solution
For this trinomial, a 6, b 19, and c 15. Because c is positive, you need
to find numbers p and q with the same sign. Because b is negative, only
negative numbers p and q need to be tried.
Student Help
Write the numbers m and n whose
STUDY TIP
Once you find the
correct binomial
factors, it is not
necessary to continue
checking the remaining
trial factors.
m and n
p and q
1, 6
2, 3
1, 15
3, 5
Trial Factors
Middle Term
(x 1)(6x 15)
(x 15)(6x 1)
(2x 3)(3x 5)
15x 6x 21x
x 90x 91x
30x 3x 19x
product is 6 and the numbers
p and q whose product is 15.
Use these numbers to write trial
factors. Then use the Outer
and Inner products of FOIL
to check the middle term.
ANSWER 䊳
6x2 19x 15 (2x 3)(3x 5).
EXAMPLE
3
Factor with a Common Factor for a, b, and c
Factor 6x2 2x 4.
Solution
The coefficients of this trinomial have a common factor 2.
2(3x2 x 2)
Factor out the common factor.
It remains to factor a trinomial with a 3, b 1, and c 2. Because c is
negative, you need to find numbers p and q with different signs.
Write the numbers m and n whose
m and n
product is 3 and the numbers
p and q whose product is 2.
p and q
1, 2
1, 2
1, 3
Use these numbers to write trial
Trial Factors
Middle Term
factors. Then use the Outer and
Inner products of FOIL to
check the middle term.
(x 1)(3x 2)
(x 2)(3x 1)
(x 1)(3x 2)
2x 3x x
x 6x 5x
2x 3x x
Remember to include the common factor 2 in the complete factorization.
ANSWER 䊳
6x2 2x 4 2(x 1)(3x 2).
Factor Trinomials
Factor the trinomial.
604
Chapter 10
4. 2x2 5x 2
5. 5x2 7x 2
6. 4x2 8x 3
7. 8r2 6r 9
8. 6x2 14x 4
9. 20x2 5x 15
Polynomials and Factoring