WorksheetsPolynomial Review
Total questions: 22
Worksheet time: 2hrs 50mins
Name
Class
Date
1.
What is the remainder: (x2-6x-11)÷(x+3)
a)
16
b)
16/(x+3)
c)
-38
d)
-38/(x+3)
e)
x+3
2.
Which of these describes end behavior for the polynomial y = 3x4 + 2x3 - 7?
a)
a
b)
b
c)
c
d)
d
3.
Find the zeros of this polynomial and describe their multiplicity.
f(x) = 3x4 - 12x2
f(x) = 3x4 - 12x2
a)
0 multiplicity 3, -2 multiplicity 1, 2 multiplicity 1
b)
-2 multiplicity 1, 2 multiplicity 1
c)
0 multiplicity 2, -2 multiplicity 1, 2 multiplicity 1
d)
3 multiplicity 4, -12 multiplicity 2
4.
Find all the zeros of the function.
f(x) = x4-3x3+5x2-27x-36
f(x) = x4-3x3+5x2-27x-36
a)
1, 2, 3, 4, 6, 12, 18, 36, -1,-2,-3,-4,-6,-12,-18, -36
b)
-1, 4, 3i, -3i
c)
-3,-1,3,4
d)
2,-2,-1,9
5.
Find all the zeros, given (x+3) is a factor
f(x) = 2x3+5x2-6x-9
f(x) = 2x3+5x2-6x-9
a)
-1,-3,2
b)
-1,-3,3/2
c)
-3,6,-2
d)
-3,2/3,-1
6.
Find a polynomial function with the given zeros: 3i and -2.
a)
P(x) = x3+2x2+9x+11
b)
P(x) = x3-2x2+9x-18
c)
P(x) = x3+2x2+9x+18
d)
P(x) = x2-3ix+2x-6i
7.
Convert the equation y= x2-2x-5 into vertex form.
a)
y= (x-1)2-6
b)
y= -(x-1)2-6
c)
y= (x+1)2-6
d)
y= -(x+6)2-1
8.
A parabola has a vertex at (-3,2).
Where is the axis of symmetry?
Where is the axis of symmetry?
a)
y = -2
b)
x = 3
c)
x = -3
d)
y = 2
9.
Where is the graph increasing?
a)
(-∞, -2.55) U (2.55, ∞)
b)
(0, ∞)
c)
(-2.55, 0) U (2.55, ∞)
d)
(-6.25, 36)
10.
If the x- intercepts of a cubic polynomial are (-2,0)(0,0)(5,0), the possible function would be:
a)
f(x) = (x - 2)(x + 5)
b)
f(x) = x(x - 2)(x + 5)
c)
f(x) = x(x + 2)(x - 5)
d)
f(x) = x2(x +2)(x - 5)
11.
Determine the y-intercept
f(x) = x3 - 5x2 - 25x + 125
f(x) = x3 - 5x2 - 25x + 125
a)
(0,0)
b)
(0,25)
c)
(0,125)
d)
(0,5)
12.
a)
Decreasing Interval
b)
Increasing Interval
c)
Constant Interval
d)
Positive Interval
e)
Negative Interval
13.
a)
Decreasing Interval
b)
Increasing Interval
c)
Constant Interval
d)
Positive Interval
e)
Negative Interval
14.
How many possible negatives solutions does the following polynomial have?
f(x) = x4 - 3x3 - 17x2 + 39x -20
a)
3 or 1
b)
3
c)
1
d)
2 or 0
15.
How many positive solutions does the following polynomial have?
f(x) =3x5 - x4 + 3x2 - 6x +11
a)
4, 2, or 0
b)
4
c)
3 or 1
d)
3
16.
a)
4th degree polynomial with a positive leading coefficient
b)
4th degree polynomial with a negative leading coefficient
c)
3rd degree polynomial with a positive leading coefficient
d)
3rd degree polynomial with a negative leading coefficient
17.
What are the asymptotes?
a)
x = -3 y = 1
b)
x = 3 y = 1
c)
x = -3 y = -1
d)
x = 3 y = -1
18.
What is/are the vertical asymptote(s)?
a)
There are no vertical asymptotes
b)
x=5
c)
x=-5
d)
x=-1/2
19.
What is/are the x-intercepts of this graph?
a)
(-2,0) and (2,0)
b)
(-2,0)
c)
(3,0)
d)
(2,0) and (3,0
20.
State the domain restrictions.
a)
x ≠ 3, -2, 6, -1
b)
x ≠ -1, 6
c)
x ≠ 3, -2
d)
No Domain Restrictions
21.
Solve the inequality graphically.
2x3 + 3x2 - 17x - 30 < 0
2x3 + 3x2 - 17x - 30 < 0
a)
(-2.5,-2) U (3,∞)
b)
(-∞,-2.5] U [-2,3]
c)
(-∞,-2.5) U (-2,3)
d)
[-2.5,-2] U [3,∞)
22.
a)
(-2, 1)
b)
(-oo, -2) u (1,2)
c)
(1,2) u (2, oo)
d)
(-oo, -2] u [1,2]
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