Day 1
Lesson Essential Question:
How can I use a variety of methods to completely factor
expressions and equations?
Multiply the following binomials.
1)
(x+3)(x-2)
x2+x-6
2)
(x-5)(x-1)
x2-6x+5
3)
(2x+5)(x+1) 2x2+7x+5
Warm Up
First
(x –6)(x –3)
Outer (x –6)(x –3)
Inner (x –6)(x –3)
Last
FOIL
(x –6)(x –3)
Now YOU try!!
First
(x +2)(x +4)
Outer (x +2)(x +4)
Inner (x +2)(x +4)
Last
FOIL
(x +2)(x +4)
What do these factors help us
find?

When a soccer ball is kicked into the air, how
long will the ball take to hit the ground?
The height h in feet of the ball after t seconds
can be modeled by the quadratic function
h(t) = –16t2 + 32t. In this situation, the
value of the function represents the height of
the soccer ball. When the
ball hits the ground, the value of the function
is zero.
Graph this on your calculator.
How would you define the zero of
a function?
Factoring when a=1
Find the zeros of f(x) = x2 – 6x + 8 by
factoring.
Factoring
Methods of Factoring Worksheet

Do #1-3 with a partner on the “Factoring
Practice” Worksheet.
Factoring Practice
1. (x + 9)(x + 2)
2. (y – 7)(y + 5)
3. (g – 6)(g + 2)
Check Your Work by Foiling!

When we use it:
◦ Usually in the form ax2 – c
◦ Both a and c are perfect squares (the square root of each
number is a whole number)
ax  c
2
( ax  c )( ax  c )
Difference of Squares

Find the zeros of f(x)=h2-81 by factoring.
Difference of Squares

Find the zeros of f(x)=49j2-144 by
factoring.
Difference of Squares
Methods of Factoring Worksheet

Do #4-10 with a partner on the “Factoring
Practice” Worksheet.
Difference of Squares Practice
Steps:
1. Multiply c and a
2. Rewrite the expression with the new value for c
3. Write (ax + )(ax + )
4. Finish “factoring” the new expression
5. Reduce each set of parentheses by any common
factors
3y  13y  4
2
Factoring (when a ≠ 1):The Welsh Method

Find the zeros of f(x) = 3x2 + 5x - 2
by factoring.
Factoring (when a ≠ 1):The Welsh Method

Find the zeros of f(x) = 7x2 - 5x - 2 by
factoring.
Factoring (when a ≠ 1):The Welsh Method
Methods of Factoring Worksheet

Do #11-16 with a partner on the
“Factoring Practice” Worksheet.
Factoring (when a ≠ 1):The Welsh Method
When we use it:
all the terms share 1 or more factors
Factoring out GCFs save us time!!!

◦
◦
4x2 – 196 = 0
(2x + 14)(2x – 14) = 0
GCF (Greatest Common Factor)
Steps:
1. Identify any common factor(s) (including the GCF)
2. Factor out the common factor(s)
3. Factor the remaining expression if possible
x  2x  3x
3
2
GCF (Greatest Common Factor)

Find the zeros of f(x) = 4x2 -32x +64
by factoring.
GCF (Greatest Common Factor)

Find the zeros of f(x)= 3x4-24x3+21x2
by factoring.
GCF (Greatest Common Factor)
Methods of Factoring Worksheet

Do #17-27 with a partner on the
“Factoring Practice” Worksheet.
GCF (Greatest Common Factor)
12x  14x  4
2
GCFs and The Welsh Method
Methods of Factoring Worksheet

Do #28-33 with a partner on the
“Factoring Practice” Worksheet.
GCFs and The Welsh Method

34. x2 + 10x + 16
NOTE: WE HAVE 3 TERMS AND a=1 !!
Picking the Right Method -?!?-

35. 5t2 + 28t + 32
NOTE: WE HAVE 3 TERMS AND a≠1 !!
Picking the Right Method -?!?-
16p2 – 9
NOTE: WE HAVE 2 TERMS WITH A MINUS IN THE MIDDLE
AND BOTH TERMS ARE A PERFECT SQUARE !!!!!!!
Picking the Right Method -?!?-

Do #36-44 with a partner on the
“Factoring Practice” Worksheet.
Picking the Right Method -?!?-
Find the zeros.
1)
x2-8x-48
2)
4x2-49
3)
2x2+x-3
Exit Ticket
Factor Completely (5 minutes)
1)
x2-13x+36
(x-4)(x-9)
2)
x2-144
(x+12)(x-12)
3)
6x2+13x+6 (3x+2)(2x+3)
Warm Up