1. Factoring ax2 + bx + c
CA 11.0

2. Objective - To factor trinomials in the form ax2 + bx + c

3. Factoring Quadratic Trinomials
The FORM is the most important thing!
ax2 + bx + c
This quadratic trinomial is in
STANDARD FORM

4. IDENTIFYING a, b, and c a is the COEFFICIENT of x2
b is the COEFFICIENT of x
and c is the constant term
a, b, and c are NUMBERS (not variables).

5. Factoring Quadratic Trinomials
Step 1: Identify a, b, c
Step 2: Create a Factor Cross
a · c b
Step 3: Solve the Factor Cross
Step 4: RE-WRITE the polynomial with FOUR TERMS
(separate the middle term into two parts)
Step 5: Factor by grouping

6. Factoring Quadratic Trinomials60
Factor 4x2 +16x + 15
a = 4, b = 16, c = 15
ac=(4)(15) = 60
4x2 +16x + 15
4x2 + 6x + 10x + 15
2x(2x + 3) + 5(2x + 3)
(2x + 3)(2x + 5)
Check  +6
+10 16

7. Factoring Quadratic Trinomials40
Factor 5x2 – 14x + 8
a = 5, b = –14, c = 8
ac=(5)(8) = 40
5x2 – 14 x + 8
5x2 – 4x – 10x + 8
x(5x – 4) + 2(–5x + 4)
x(5x – 4) + 2(–1)(5x – 4)
x(5x – 4) – 2(5x – 4)
(5x – 4)(x – 2)
Check  –4
–10
–14

8. Factoring Quadratic Trinomials
Factor 2x2 – 7x – 15
a = 2, b = –7, c = – 15
ac=(2)(– 15) = – 30
2x2 –7x – 15
2x2 – 10x + 3x – 15
2x(x – 5) + 3(x – 5)
(x – 5)(2x + 3)
Check 
–30
–10 +3 –7

9. Factoring Quadratic Trinomials
Factor – 2x2 – 15x – 7
Since ALL the terms are negative, we should start by factoring out
(– 1)
(– 1) (2x2 + 15x + 7)

10. Factoring Quadratic Trinomials
Factor (– 1) (2x2 + 15x + 7)
a = 2, b = 15, c = 7
ac=(2)(7) = 14
(– 1) (2x2 + 15x + 7)
(– 1) (2x2 + 14x + 1x + 7)
(– 1) [2x(x + 7) + 1(x + 7)]
(– 1)(x + 7)(2x + 1)
Check  14
+14 +1 15