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Chapter 5
Section 4
Factoring Quadratic Expressions

Factoring – rewriting an expression as the
product of its factors

Greatest Common Factor of an expression –
GCF is the common factor with the greatest
coefficient and the greatest exponent



The largest number and variable that will go into
everything
Binomial – an expression with two terms
ex: 2x+3
Trinomial – an expression with three terms
ex: x2 + 5x -94
Factor each expression.
a) 4x  20 x  12
2

What is the largest number
common to all terms?


b) 9n  24n
2
What is the greatest
exponent on the variables
that is common to all?


Write it on the outside of the
parenthesis
Write it beside the first
number.
In parenthesis write what is
left when you divide the
term by the expression
written.
Try These Problems.
a) 9x  3x  18 c) 4w  2w
2
2
3(3x  x  6)
2
b) 7 p  21
2
7( p  3)
2
2w(2 w  1)
d) 5 p  15 p
3
2
5 p ( p  3)
2
Public Service Announcement
There are many ways to factor. You learned in
Alg I how to factor. Pay attention, if the
method taught then did not click, hopefully
one of today’s methods will. I will not specify
how you have to factor, as long as you are
doing it correctly. Factoring DOES NOT GO
AWAY, we use it all year and for the rest of
math. Be sure you understand how or seek
out help now!!!
“Formal Factoring”
AKA: factor and sum method
note this will always work
ax2 + bx + c
Find factors of a∙c (the first times the last)
2. Find the sum of the factors
3. Choose the factors whose sum is b
4. Rewrite the linear term using the factors you
found
5. Take the GCF out of the first two terms, then the
second leaving two identical binomials
6. Rewrite using the identical binomial and what is
on the outside as the other binomial
Check: (FOIL) Multiply the binomials
1.
3x2 - 16x + 5
Step 1:
Factors of
Step 2:
Step 4:
Step 5:
Step 6:
Check:
Sum of
Factors
X2 + 8x + 7
Factors of
Sum of
Factors
X2 - 17x + 72
Factors of
Sum of
Factors
X2 - x - 12
Factors of
Sum of
Factors
“Informal Factoring”
ax2 + bx + c



What numbers multiply to give me a? c?
What signs should I use?
Do the combinations add to give me b?
x  14 x  40
2
a) x  11x  24
2
b) x  4 x  5
2
This one has a catch so watch carefully
2x  7x  6
2
Factor. (you can use any method)
a) x  12 x  32
b) x  3x  10
c) x  7 x  12
d) 4x  7 x  3
2
2
2
2
Factoring Day 2: Special
Expressions

There are some expressions that can be
factored by following patterns
Perfect Square Trinomial

The product when you square a binomial
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2

This pattern can be used to factor:
9x2 – 42x + 49
4x2 + 12x + 9
Difference of Two Squares

(a - b)(a + b) = a2 - b2

This pattern can be used to factor:
x2 – 64
4a2 - 49