Pre-Calculus Polynomial Worksheet
For #1-4, use the Leading Coefficient Test to determine the end behavior of the graph of the given
polynomial function. Then use this end behavior to match the polynomial function with its graph.
1.
f(x) x3x22x
2.
f(x)x66x49x2
3.
f(x)x55x34x
4.
f(x) x41
a. b. c. d.
For #5-6, find the zeros for each polynomial function and give the multiplicity of each zero. State
whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero.
5.
f(x) 2(x1)(x2)2(x5)3
6.
f(x)x35x225x125
For # 7-8,
a. Use the Leading Coefficient Test to determine the graph’s end behavior.
b. Determine whether the graph has y-axis symmetry, origin symmetry, or neither.
c. Graph the function.
7.
f(x)4xx3
8.
f(x) x46x39x2
Divide using long division.
9.
4x33x22x1
x1
10.
10x326x217x13
5x3
11.
4x46x33x1
2x21
Divide using synthetic division.
12.
3x411x320x27x35
x5
13.
3x42x210x
x2
14.
x26x6x3x4
6x
0 at (x =1)/ multiplicity 1 (crosses x-axis)
0 at (x = -2) / multiplicity of 2( touches x axis
and turns around)
0 at (x=-5)/ multiplicity of 3/
0 at ( x = -5) / multiplicity of 1 and crosses x
axis
0 at (x = 5)/ multiplicity of 2 and touches x
and turns around.
x = Inf
f(x) = -inf
No Symmetry
Graph.
x = infinity
f(x) = - inf
no symmetry
Graph:
Long Division and Synthetic division Work attached separately
