Name:__________________________
Polynomials – Connecting factors, solutions, and x-intercepts
Do you want me to Solve or find x-intercepts?
Completely Factor the
expression
1. Example:
9 x 2 12 x
3x 3 x 4 Solve the equation
2. Example:
9 x 2 12 x 0
3x 3 x 4 0
3 x 0 or 3 x 4 0
4
x 0 or x 3
Determine the x-intercepts
of the graph
3.
Example:
y 9 x 2 12 x
0, 0 6.
y
§ 4 ·
and ¨ , 0 ¸
© 3 ¹
2
2x 7x
x 2 12 x 35 0
9.
y
x 2 12 x 35
11.
x 2 6 x 72
12. y
x 2 6 x 72
4 x 2 12 x 8
14.
4 x 2 12 x 8 0
15.
y
4 x 2 12 x 8
4 x 2 4 x 35
17.
4 x 2 4 x 35 0
18.
y
4 x 2 4 x 35
4.
2x2 7 x
5.
2x2 7 x
7.
x 2 12 x 35
8.
10.
x 2 6 x 72
13.
16.
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0
0
43
Use a graphing calculator to solve #19 - #22. Include a sketch that supports your
conclusion.
19.
20.
0.5 x 2 1.75 x 0
0.5 x 4 1.5 x 3 5 x 2 12 x 0
(Note: This equation is difficult to solve
with factoring. Use an appropriate graph)
21.
x2 6x 4 0
(Note: This equation cannot be solved by
factoring. Use an appropriate graph.
Round your solutions to the nearest tenth)
x3 3x 2 6 x 8 0
22.
23. Using your reasoning
powers derived from this lab
draw a line from the
equation to the graph that it
matches.
6 x 2 16 x 6
2 x 4 x3 31x 2 26 x 24
3 x 3 3 x 2 36 x
2x 3
44
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