Math 2 Honors
Name ____________________________
Lesson 2-4: Factoring – The Greatest Common Monomial Factor
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)  8x 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:
OVER 
Page 2
Factor the following functions completely.
1. f ( x)  10 x  80
2. g ( x)  9 x 2  36
3. h( x)  x 2  x
4. r ( x)  6 x 2  36 x
5. s( x)  15 x 2  5
6. t ( x)  2 x 2  7 x
Now go back and graph each expression in your calculator, one at a time. For each expression, do the
following:
 Use the calculator to identify the x-intercept(s).
 Make a sketch & label the x-intercepts.
1.
2.
3.
4.
5.
6.

What is the connection between the factors and x-intercepts?
NOTES:
HOMEWORK
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.
i( x)  100 x  800 x 2
17.
n( x)  45 x 2  25 x
OVER 
18.
l ( x)  20 x 2  200
19.
m( x)  2 x 2  28 x
Review: Use the distributive property to write the given expressions in standard form:
2
20.
4 x  2 x  5
Circle one: Maximum
22.
21.
Minimum
9  2 x 1  4 x  5  3x 
Circle one: Maximum
24.
ax  bx  c
Circle one: Maximum
Circle one: Maximum
23.
Minimum
4 x2  3  x  4   2  x 
Minimum
5  x  2 x  8
7  3x 2  4 x  2 
Circle one: Maximum
25.
Minimum
Minimum
10  2 x  8   8  3 x 2  4 x 
Circle one: Maximum
Minimum