1. 5.3 Factoring Quadratics

2. Factoring : ax2 + bx + c
To factor an expression of the form ax2 + bx + c
Look for integers r & s such that r · s = a · c and r + s = b.
Replace the bx term with rx + sx.
Group and factor.

3. Examples of Factoring : ax2 + bx + c
Factor the following: x2 + 7x + 10
mult. to be ac = 10
add to be b = 7 x
(x ) + ( )
(x ) ( x )
(x ) ( x )

4. Examples of Factoring : ax2 + bx + c
Factor the following: x2 – 3x – 10
mult. to be ac = -10
add to be b = -3 x
(x ) + ( )
(x ) ( x )
(x ) ( x )

5. Examples of Factoring : ax2 + bx + c
Factor the following: 2x2 + 9x + 10
mult. to be ac = 20
add to be b = 9 2x
(2x ) + ( )
( x ) ( x )
( x ) ( x )

6. Factoring the Difference of Two Squares
Multiply the following: (x + 3) (x – 3)
Rule for Factoring Difference of Squares:
a2 – b2 = (a + b) ( a – b)
Example 1
Factor the following: x2 – 25
Example 2
Factor the following: x4 – 16

7. Factoring Perfect-Square Trinomials
Rules for Factoring Perfect-Square Trinomials:
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
Example 1: 4x2 – 24x + 36

8. Zero-Product Property
If pq = 0, then p = 0 or q = 0.
Example 1:
What is the solution to the equation (x + 5)(x + 1) = 0?