Math 2
Lesson 3-3: Factoring Quadratics
Name_________________________________
Date _______________________________
Learning Goals:

I can write quadratic expressions in equivalent expanded form or factored form.
Part 1:
Factoring means taking an expression and rewriting it as a product. For example, to factor 12, you can
write:
12  4  3 or 12  6  2 or 12  12  1 or 12  4  3 or 12  6  2 or 12  12  1
It is useful to factor quadratics, because then x-intercepts are easily identifiable from the equation in
factored form.
In yesterday’s activity, you reviewed how to expand expressions that were in factored form. For example:
=
Factored form
Expanded form
To factor a quadratic in expanded form, we have to reverse the process.
When the leading coefficient of the quadratic expression is positive one,
we simply “play” the PRODUCT-SUM game.
Let’s try these examples. Factor the following expressions:
1.
x 2  22 x  21
2.
x 2  10 x  24
3.
x 2  10 x  25
4.
x 2  7 x  30
5.
x 2  13 x  42
6.
x 2  36
How can you check to make sure you have factored correctly?
Part 1 Homework: Complete the problems on the back of this worksheet.
OVER 
Part 1 Homework:
Directions: Factor the following expressions completely, if possible.
Part 2
When the leading coefficient is of a quadratic is NOT 1, we can no longer rely on the Product/Sum
game.
2x2 + 3x – 20 =
Factor the following:
(
)(
)
Let’s try these examples. Factor the following expressions:
3 x 2  23 x  30
7.
8.
6 x2  5x  4
9.
4 x 2  25 x  21
10.
36 x 2  25
11.
2 x 2  11x  15
12.
x 2  9 x  20
How can you check to make sure you have factored correctly?
Day 2 Homework: Complete the problems on the back of this worksheet.
OVER 
Part 2 Homework:
Directions: Factor the following expressions completely, if possible.
15)
16)