4.4 Factoring Quadratic Expressions
Name: __________________
Objectives:
Students will be able to find common binomial factors of quadratic expressions
and factor special quadratic expressions.
-Greatest Common Factor (GCF): The largest number and/
or variable that is a factor of all terms.
GOLDEN RULE OF FACTORING! Always look for a greatest common
factor (GCF) before doing any other type of factoring.
Examples: Factor out the GCF.
1.) 4x2 - 2x
Oct 2­8:54 AM
2.) 5y3 + 10y - 15y6
4.) 7(x + 2) -2x(x + 2)
3.) 40xy2 + 10x2y + 50x4y3
5.) x(x - 4) + 2(x - 4)
Oct 2­8:56 AM
1
Do you remember how to multiply out (x + 2)(x + 4)?
Now, we'll reverse this process.
To factor x2 + bx + c, find factors of c that add up to b.
Examples: Factor. If the expression cannot be factored, say "does not
factor."
1.) x2 + 4x + 3
2.) x2 - 9x + 20
3.) x2 + 3x - 12
4.) x2 - 7x + 10
Oct 24­12:21 PM
5.) x2 - 4x - 12
6.) m2 + 8m - 65
7.) p2 + 8p + 16
Difference of Two Squares
a2 - b2 = (a + b)(a - b)
Examples: Factor.
1.) x2 - 4
4.) x4 - 16
2.) a2 - 81
3.) 100 - x2
5.) 16x2 - 1
Oct 24­12:28 PM
2
Factor by Grouping
2.) 2x3 - 4x2 - 5x + 10
1.) 3x3 + 12x2 + x + 4
Steps to factoring ax2 + bx + c: (Rewrite Method)
1.)
2.)
3.)
4.)
Multiply a and c.
Find factors of ac that add up to b.
Rewrite bx using those factors.
Factor by grouping.
Oct 2­8:55 AM
Examples: Factor.
1.) 16x2 + 8x + 1
2.) 3x2 - 7x + 4
3.) 4y2 - 5y - 4
4.) 4x3 - 2x2 - 6x
Oct 2­10:10 AM
3