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WorksheetsCubic equation
Total questions: 24
Worksheet time: 2hrs 32mins
Name
Class
Date
1.
Which of the following is the graph of y=(x−2)3−4
a)
b)
c)
d)
2.
What is the y-intercept of f(x) = (x + 2)3 - 6?
a)
(2, 0)
b)
(-0.5, 0)
c)
(0, 2)
d)
(0, -0.5)
e)
None
3.
Solve for x:
(3x + 1)3 = 64
a)
-1
b)
6
c)
1
d)
No real solution
4.
Determine the roots of the polynomial.
f(x) = (x+1)(x-4)(x+2)
f(x) = (x+1)(x-4)(x+2)
a)
1, 4, 2
b)
-1, -4, -2
c)
1, -4, 2
d)
-1, 4, -2
5.
Determine the roots of the polynomial.
f(x) = (x-2)(x+3)2
f(x) = (x-2)(x+3)2
a)
2, 3
b)
2, -3
c)
-2, 3
d)
-2, 3, 3
6.
What are the x-intercepts of the following function?
y = (x - 1)(x +3)(x - 4)
y = (x - 1)(x +3)(x - 4)
a)
1, 3 and 4
b)
2, 1, -3, and 4
c)
-1, 3, and -4
d)
1, -3, and 4
7.
What are the x-intercepts of the following function?
y = (x - 1)(x +3)(x - 4)
y = (x - 1)(x +3)(x - 4)
a)
1, 3 and 4
b)
2, 1, -3, and 4
c)
-1, 3, and -4
d)
1, -3, and 4
8.
What are the
zeros of the polynomial
y = (x + 4)(x + 1)(x - 3)?
zeros of the polynomial
y = (x + 4)(x + 1)(x - 3)?
a)
-4, -1, 3
b)
3, -3, 4, 1
c)
4, 1, -3
d)
3, -4, -1, 3
9.
What is the domain ALL cubic functions expressed as an inequality?
a)
(-∞,∞)
b)
-∞<x< ∞
c)
(-∞, 0]
d)
-∞<y< ∞
10.
Using you CALCULATOR, What are the zeros of the function f(x) = -2x3 - 4x2 + 6x?
a)
x = 0, -2, -3, 1
b)
x = -3, 1
c)
x = 0, 3, -1
d)
x = 0, -3, 1
11.
Which set of factors has x-intercepts at 5, -1, 2?
a)
(5x)(-1x)(2x)
b)
(x-5)(x+1)(x-2)
c)
(x-5)(x-1)(x-2)
d)
(x+5)(x-1)(x+2)
12.
What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x3 - 5x2 + 2x - 10
p(x) = x3 - 5x2 + 2x - 10
a)
0
b)
2x-10
c)
-2x-10
d)
2x+10
13.
Is (x-4) a factor of (x3 +x2 -16x-16)?
a)
YES
b)
NO
14.
Which term is missing in this problem?
(2x3 + 5x2 + 9) ÷
(x + 3)
(2x3 + 5x2 + 9) ÷
(x + 3)
a)
x4
b)
x3
c)
x2
d)
x
15.
Decide if (x-3) is a factor of 3x3+10x2-x-12
a)
Yes, it is a factor!
b)
No, it is not a factor!
16.
Find all the zeros, given that f(-3) = 0
f(x) = 2x3+5x2-6x-9
f(x) = 2x3+5x2-6x-9
a)
-1,-3,-3
b)
-1,-3,3/2
c)
3,3,3
d)
-3,2/3,-1
17.
Is (x-7) a factor of (x2-5x+14)?
a)
Yes
b)
No
18.
Which binomial is a factor of
f(x)= x3 -6x2 +3x +10?
f(x)= x3 -6x2 +3x +10?
a)
x + 1
b)
x + 2
c)
x + 5
d)
x + 10
19.
What are the three factors for
(x3 +7x2 +7x -15) ÷ (x -1)?
(x3 +7x2 +7x -15) ÷ (x -1)?
a)
(x-1) (x+5) (x-3)
b)
(x-1) (x+5) (x + 3)
c)
(x+1) (x+5) (x-3)
d)
(x+1) (x-5) (x-3)
20.
Given P(x) = 3x3 + 5x2 – 4x -8, what is the value of P(3)?
a)
120
b)
115
c)
109
d)
106
21.
1. If P( -4) = 0, which of the following statements is true about P(x)?
a)
x+4 is a factor of P(x)
b)
P(x) = 0, has four negative roots
c)
4 is a root of P(x) = 0
d)
P(0) = - 4
22.
Given P(x) = 2x4 + x3 –3x2 – x – 15. What is the value of P(2).
a)
25
b)
17
c)
11
d)
9
23.
x – 1 is a factor of 2x3 – x2 + 2x - 3
a)
b)
24.
If the remainder of a given polynomial expression is 0, then (x –r) is NOT a factor of P(x).
a)
b)
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