1. Warm Up #8 Find the product 2. (5m + 6)(5m – 6) 1. (4y – 3)(3y + 8)
3. (4q – 5)2
4. Solve x2 – x – 30 = 0.
16q2 – 40q + 25
(x – 6 )(x + 5) = 0
x = 6 or x = -5

3. EXAMPLE 1
Factor 5x2 – 17x + 6.
Factors of +30
That add up to -17
(5x )(x )
– 2
– 3
-15 and -2
Factor 3x2 + 20x – 7.
Factors of -21
That add up to + 20
(3x )(x )
– 1
+ 7
21 and -1

4. GUIDED PRACTICE GUIDED PRACTICE for Examples 1 and 2 1. 7x2 – 20x – 3
Factor the expression. If the expression cannot be factored, say so.
x2 – 20x – 3
z2 + 16z + 3
Factors of -21 that add up to -20
Factors of 15 that add up to 16
-21 and 1
15 and 1
(7x )(x )
+ 1
– 3
(5z )(z )
+ 1
+ 3
x2 + 5x – 12
w2 + w + 3
Factors of -36 that add up to 5
Factors of 6 that add up to 1
9 and -4
There are none
cannot be factored
(3x )(x )
– 4
+ 3

5. GUIDED PRACTICE GUIDED PRACTICE for Examples 1 and 2 6. 4x2 – 9x + 2
u2 + 12u + 5
Factors of 20 that add up to 12
Factors of 8 that add up to -9
10 and 2
-8 and -1
(4u )(u )
(4x )(x )
– 1
– 2
(2u )(2u )
+ 1
+ 5
(2x )(2x )

6. Recall: x2 – y2 = (x – y)(x + y)
Example: 4x2 – 25 = (2x – 5)(2x + 5)
Recall: x2 + 2xy + y2 = (x + y)2
Example: 9x2 + 30x + 25 = (3x + 5)2

7. Factor with special patterns
EXAMPLE 3
Factor with special patterns
Factor the expression.
a. 9x2 – 64
= (3x – 8)(3x + 8)
Difference of two squares
b. 4y2 + 20y + 25
= (2y + 5)2
Perfect square trinomial
c w2 – 12w + 1
= (6w – 1)2
Perfect square trinomial

8. EXAMPLE 4
Recall: GCF (Greatest Common Factor)
Factor the expression.
a. 5x2 – 45
= 5(x2 – 9)
= 5(x + 3)(x – 3)
b. 6q2 – 14q + 8
= 2(3q2 – 7q + 4)
= 2(3q – 4)(q – 1)
c. –5z2 + 20z
= –5z(z – 4)
d. 12p2 – 21p + 3
= 3(4p2 – 7p + 1)

9. Solve quadratic equations
EXAMPLE 5
Solve quadratic equations
Solve (a) 3x2 + 10x – 8 = 0
a. 3x2 + 10x – 8 = 0
Write original equation.
Factors of -24 that add up to 10
Factor.
12 and -2
(3x )(x ) = 0
– 2
+ 4
3x – 2 = 0
or x + 4 = 0
Zero product property
3x = 2
Solve for x.
or x = –4
x = 23

10. Solve quadratic equations
EXAMPLE 5
Solve quadratic equations
(b) 5p2 – 16p + 15 = 4p – 5.
b. 5p2 – 16p + 15 = 4p – 5.
Write original equation.
5p2 – 20p + 20 = 0
Write in standard form.
5(p2 – 4p + 4) = 0
Factor out a 5.
p2 – 4p + 4 = 0
Divide each side by 5.
(p – 2)2 = 0
Factor.
p – 2 = 0
Zero product property
p = 2
Solve for p.