1. Factoring Trinomials of the Form x2 + bx + c
6.2
Factoring Trinomials of the Form x2 + bx + c
1. Factor trinomials of the form x2 + bx + c.
2. Factor out a monomial GCF, then factor the trinomial of the form x2 + bx + c.

2. Factoring Trinomials of the Form x2 + bx + c
Study these products to see some patterns that might be helpful in factoring trinomials.
Factors that ADD
Add middle terms
Signs are the same.
Subtract middle terms.
Signs are different.
Factors that subtract.

3. Signs are the same.
Factors that ADD
Signs are different.
Factors that SUBTRACT.

4. Factor: + + Check by foiling! Signs are the same. Factors that ADD.
Both positive.
Signs are the same.
Factors that ADD. + +
Check by foiling!

5. Factor: – – Check by foiling! Signs are the same. Factors that ADD.
Both negative.
Signs are the same.
Factors that ADD. – –
Check by foiling!

6. Factor: + – Check by foiling! Larger factor is negative.
Signs are different.
Factors that SUBTRACT. + –
Check by foiling!

7. Factor: – + Check by foiling! Larger factor is positive.
Signs are different.
Factors that SUBTRACT. – +
Check by foiling!

8. Factor:
Signs are the same.
Factors that ADD.
Prime polynomial

9. Factoring a trinomial with two variables
Outside:
Inside:
The double variable in the middle term comes from multiplying the outside and inside terms.

10. Factor: + – Check by foiling! Larger factor is negative.
Signs are different.
Factors that SUBTRACT. + –
Check by foiling!

11. Factor:
Check by foiling!

12. Copyright © 2011 Pearson Education, Inc.
Factor. x2 + 5x – 36
a) (x + 3)(x – 12)
b) (x – 3)(x + 12)
c) (x + 9)(x – 4)
d) (x – 9)(x + 4)
Copyright © 2011 Pearson Education, Inc.
6.2

13. Copyright © 2011 Pearson Education, Inc.
Factor. x2 + 5x – 36
a) (x + 3)(x – 12)
b) (x – 3)(x + 12)
c) (x + 9)(x – 4)
d) (x – 9)(x + 4)
Copyright © 2011 Pearson Education, Inc.
6.2

14. Copyright © 2011 Pearson Education, Inc.
Factor completely. 5rs3 – 10rs2 – 40rs
a) 5rs(s2 – 2s – 8)
b) 5rs(s2 + 2s – 8)
c) 5rs(s + 2)(s – 4)
d) 5rs(s – 2)(s + 4)
Copyright © 2011 Pearson Education, Inc.
6.2

15. Copyright © 2011 Pearson Education, Inc.
Factor completely. 5rs3 – 10rs2 – 40rs
a) 5rs(s2 – 2s – 8)
b) 5rs(s2 + 2s – 8)
c) 5rs(s + 2)(s – 4)
d) 5rs(s – 2)(s + 4)
Copyright © 2011 Pearson Education, Inc.
6.2