1. Warm-Up #7 Find the product 1. (m – 8)(m – 9) m2 – 17m + 72 ANSWER
2. (z + 6)(z – 10)
ANSWER
z2 – 4z – 60

3. y y + 4 + 2 ( )( ) ( )( ) ( )( ) ( )( ) First sign remains the same
( )( )
If second sign is + then the
signs are the same
If second sign is - then the
signs are different
Factors of 8
( )( )
That add up
To 6
( )( )
( )( )

4. Make sure it's in descending order
( )( )
( )( )

5. ( )( )
( )( )
( )( )
( )( )

6. GUIDED PRACTICE
for Example 1
Factor the expression. If the expression cannot be factored, say so.
1. x2 – 3x – 18
2. n2 – 3n + 9
3. r2 + 2r – 63
ANSWER
ANSWER
ANSWER
(x – 6)(x + 3)
cannot be factored
(r + 9)(r –7)

7. Difference of Squares

8. Factor with special patterns
EXAMPLE 2
Factor with special patterns
Factor the expression.
a. d d + 36
(d + 6)(d + 6)
Look for perfect squares
(d + 6)2
Perfect square trinomial
b. z2 – 26z + 169
Look for perfect squares
(z – 13)2
Perfect square trinomial

9. GUIDED PRACTICE
for Example 2
1. w2 – 18w + 81
(w – 9)2
2. y2 + 16y + 64
(y + 8)2

10. Find the zeros of quadratic functions.
EXAMPLE 5
Find the zeros of quadratic functions.
Find the zeros of the function by rewriting the function in intercept form.
Another name for zeros is x-intercepts
a. y = x2 – x – 12
a. y = x2 – x – 12
Write original function.
= (x + 3)(x – 4)
Factor.
The zeros of the function are –3 and 4.
Check Graph y = x2 – x – 12. The graph passes through (–3, 0) and (4, 0).

11. Find the zeros of quadratic functions.
EXAMPLE 5
Find the zeros of quadratic functions.
b. y = x2 + 12x + 36
Write original function.
= (x + 6)(x + 6)
Factor.
The zeros of the function is –6
Check Graph y = x2 + 12x The graph passes through ( –6, 0).

12. GUIDED PRACTICE
GUIDED PRACTICE
for Example 5
for Example
Find the zeros of the function by rewriting the function in intercept form.
y = x2 + 5x – 14
ANSWER
–7 and 2
y = x2 – 7x – 30
ANSWER
–3 and 10
12. f(x) = x2 – 10x + 25
ANSWER 5