1. 4.3 Warm-up vertex = (-1, -8) Graph: y = 2 (x + 3) (x – 1)
axis of symmetry: x = -1
Write y = 2(x – 3)2 + 9 in Standard Form
hint: use FOIL
Answer: y = 2x2 – 12x + 27

2. Solve equations of the form: x2 + bx + c = 0 by Factoring.
4.3
Solve by Factoring
Solve equations of the form: x2 + bx + c = 0 by Factoring.
Key Vocabulary:
Monomial is one expression. Examples: 4 x x2
5x2
Binomial is two expressions. Examples: x + 4
y2 + 5
Trinomial is three expressions. Examples: x2 + 11x - 28
x2 - x + 3

3. 4 ∙ 3 = 12 factor factor product
Do you remember
= 5 addend addend sum
as well as
4 ∙ = factor factor product
So,
12 = (4)(3)
product = (factor) (factor)

4. How do we simplify this expression: 2x2 + 6x 2x (x + 3)
One more reminder
How do we simplify this expression:
2x2 + 6x
2x (x + 3)

5. Now we are going to begin with the PRODUCT and find the FACTORS.
In the previous chapter we used FOIL to write (x + 3) (x – 2) as x2 – x – 6:
(x + 3) (x – 2) = x2 – 2x + 3x – 6
= x2 – x – 6
Notice our product is: x2 – x – 6
And our factors are: (x + 3) (x – 2)
Factor the expression:
x2 – x – = ( ) ( )
(x ) (x )
(x 3) (x 2)
(x + 3) (x – 2)
Now we are going to begin with the PRODUCT and find the FACTORS.

6. NO FUSS FACTORING Factor the Expression: x2 - 9x + 20
Goal: We want x2 - 9x + 20 = ( )( )
1. List factors of , 20 ( 1 x 20 = 20)
2, 10 ( 2 x 10 = 20)
4, 5
-1, -20
-2, -10
-4, -5
Which factors when added together equal -9?
1 + 20= 21
2 + 10= 20
= 9
(-4) + (-5) = -9
Now we use those factors -4, -5 to complete factoring our expression (x ) (x )
(x – 4) (x – 5)
Check answer using FOIL

7. EXAMPLE 1 Factor the expression. a. x2 + 11x + 28 b. x2 – 4x – 12
Factors of 28:
Sum of factors to equal 11:
1, 28
= 29 no
2, 14
= 16 no
4, 7
= 11 yes
-1, -28
Once you find it,
-2, -14
don’t need to
-4, -7
check the rest!
Factors of -12:
Sum of factors to equal -4:
-1, 12
= 11 no
-2, 6
= 4 no
-3, 4
= 1 no
3, -4
3 + (-4) = -1 no
2, -6
2 + (-6) = - 4 yes
1, -12
x2 + 11x + 28 factored is:
(x )(x )
(x + 4)(x + 7)
x2 – 4x – 12 factored is:
(x + 2)(x – 6)

8. EXAMPLE 1 c. x2 + 3x – 12 d. x2 – 49 x2 – 49 factored is:
Factors of -12:
Sum of factors to equal 3:
-1, 12
= 11 no
-2, 6
= 4 no
-3, 4
= 1 no
3, -4
3 + (-4) = -1 no
2, -6
2 + (-6) = -4 no
1, -12
1 + (-12) = -11 no
Factors of -49: m , n
Sum of factors: m + n
-1, 49
= 48 no
-7, 7
= 0 yes
7, -7
1, -49
x2 – 49 factored is:
(x – 7)(x + 7)
This is called a difference of squares because we could write: x2 – 49 as x2 – 72.
Notice that there are no factors that sum to 3.
So, x2 + 3x – 12 cannot be factored.
Whenever we have an equation by the form: a2 – b The factorization is: (a – b) (a + b)

9. GUIDED PRACTICE
Factor the expressions.
e. x2 – 3x – 18
(x – 6) (x + 3)
f. n2 – 3n + 9
n2 – 3n + 9 cannot be factored
g. d d + 36
(d + 6) (d + 6) = (d + 6)2
h. x2 – 26x + 169
(x – 13)2

10. Solve the equation x2 – 5x – 36 = 0.
Factor the equation:
x2 – 5x – 36 = 0
(x – 9) (x + 4) = 0
Set each factor equal to zero:
(x – 9) = or (x + 4) = 0 zero product property
Solve for x:
x – 9 = 0 x + 4 = 0
x = 9 or x = -4
4. The solution is: x = 9 or x = -4

11. 1. Solve the equation x2 – x – 42 = 0.
GUIDED PRACTICE
1. Solve the equation x2 – x – 42 = 0.
x2 – x – 42 = 0
(x + 6)(x – 7) = 0
x + 6 = or
x – 7 = 0
x = – 6 or
x = 7
2. Find the zeros of the function y = x2 – 7x – 30
= (x + 3) (x – 10)
Set equal to 0 and solve for x:
x = - 3 and x = 10
The zeros of the function are – 3 and 10

12. Homework: p. 255: #3-60 (EOP) GUIDED PRACTICE GUIDED PRACTICE
3. Find the zeros of the function: f(x) = x2 – 10x + 25
= (x – 5) (x – 5)
The zero of the function is 5
Check Graph f(x) = x2 – 10x The graph passes through ( 5, 0).
Homework: p. 255: #3-60 (EOP)