1. EXAMPLE 1
Factor when b is negative and c is positive
Factor 2x2 – 7x + 3.
SOLUTION
Because b is negative and c is positive, both factors of c must be negative. Make a table to organize your work.
You must consider the order of the factors of 3, because the x-terms of the possible factorizations are different.

2. Factor when b is negative and c is positive
EXAMPLE 1
Factor when b is negative and c is positive
–x – 6x = –7x
(x – 3)(2x – 1)
3, 1
1, 2
–3x – 2x = –5x
(x – 1)(2x – 3)
–1, –3
1,2
Middle term
when multiplied
Possible
factorization
Factors
of 3
Factors of 2
Correct
2x2 – 7x + 3 = (x – 3)(2x – 1)
ANSWER

3. EXAMPLE 2
Factor when b is positive and c is negative
Factor 3n2 + 14n – 5.
SOLUTION
Because b is positive and c is negative, the factors of c have different signs.

4. Factor when b is negative and c is positive
EXAMPLE 2
Factor when b is negative and c is positive
n – 15n = –14n
(n – 5)(3n + 1)
–5, 1
1, 3
–n + 15n = 14n
(n + 5)(3n – 1)
5, –1
5n – 3n = 2n
(n – 1)(3n + 5)
–1, 5
–5n + 3n = – 2n
(n + 1)(3n – 5)
1, –5
Middle term
when multiplied
Possible
factorization
Factors of –5
Factors of 3
Correct
3n2 + 14n – 5 = (n + 5)(3n – 1)
ANSWER

5. GUIDED PRACTICE
for Examples 1 and 2
Factor the trinomial.
t2 + 8t + 4
(t + 2)(3t + 2)
ANSWER
s2 – 9s + 5
(s – 1)(4s – 5)
ANSWER
h2 + 13h – 7
(h + 7)(2h – 1)
ANSWER