Math 2
Lesson 2-4: Factoring – The Greatest Common Monomial Factor
Name ____________________________
Date _____________________________
Learning Goals:
 I can rewrite equivalent expressions by distributing (expanding) and factoring.
 I can write and graph a quadratic defined by an expression in different but equivalent forms (e.g.
standard form and factored form) to reveal and explain different properties of the function.
Consider the following two functions:
f ( x)  8 x 2  36 x
1.
Is f(x) linear or quadratic? Explain.
2. Does f(x) have a maximum or minimum?
and
g ( x)  4 x(2 x  9)
Is g(x) linear or quadratic? Explain.
If g(x) is quadratic, does it have a maximum
or minimum?
3. Graph both functions in your calculator in the same window. What do you notice? Why do you
think this happened?
4. Use your calculator to find the x-intercepts of the functions. Make a sketch of the graph and label
the x-intercepts.
NOTES:
Examples:
Factor the following expressions. Then use the Zero Product Property to find the x-intercepts of the
function (also called the zeros of the function).
I.
f  x   2x2  6x
II.
g  x   20x  8x2
Practice
Factor the following expressions. Then use the Zero Product Property to find the x-intercepts of the
function. Use your calculator to verify your answers.
1. f  x   10 x2  80 x
2. g  x   x2  x
3. h  x   9 x2  36
4. k  x   6 x2  36 x
5. y  2 x 2  7 x
6. y  15x2  5
Math 2
2-4 Practice
Name__________________________________
Factor each expression below, if possible.
4 x 2  12
1.
2.
4 x  14 x 2
3.
11  19x 2
4.
11x  19 x 2
5.
25x 100
6.
6  x  3  2  6  3x 
7.
10  2 x 1  4 x  5  3x 
8.
4 x 2  100 x
9.
x2 
The following functions are already in factored form. Find their x-intercepts WITHOUT graphing.
10.
f ( x)  10 x( x  19)
11.
g ( x)  (2 x  9) x
12.
h( x)  8 x( x  1)
13.
g ( x)  ( x  17)( x  13)
Factor the following functions. Then use the factors to find the x-intercepts WITHOUT graphing.
14.
h( x )  x 2  2 x
15.
e( x)  6 x  12
16.
n( x)  45 x 2  25 x
17.
m( x)  2 x 2  28 x
Review: Use the distributive property to write the given expressions in general quadratic form. Then
decide if the function has a maximum or minimum.
2
.
f  x   ax  bx  c
18.
y  4 x  2 x  5
Circle one: Maximum
20.
19.
Minimum
y  4 x2  3  x  4   2  x 
Circle one: Maximum
Minimum
f  x   5  x  2 x  8
Circle one: Maximum
21.
Minimum
f  x   10  2 x  8   8  3x 2  4 x 
Circle one: Maximum
Minimum