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WorksheetsFundamental Theorem of Algebra and Finding all zeros
Total questions: 20
Worksheet time: 54mins
Name
Class
Date
1.
Find all rational zeros
f(x) = x3-3x2-x+3
f(x) = x3-3x2-x+3
a)
2,4,3
b)
-1,1,3
c)
3,2,1
d)
4,5,6
2.
Find all rational zeros
f(x) = x3-5x2-2x+24
f(x) = x3-5x2-2x+24
a)
-2,1,0
b)
-2,-3,-4
c)
4,3,-2
d)
0,0,0
3.
Find all rational zeros
f(x)= x3-4x2-17x+60
f(x)= x3-4x2-17x+60
a)
5,-4,3
b)
3,1,2
c)
3,4,-5
d)
3,3,3
4.
Is (x-8) a factor of
(x3-15x2+51x+30)
(x3-15x2+51x+30)
a)
No
b)
Yes
5.
Is (x-2) a factor of
(x3+2x2-4x-8)
(x3+2x2-4x-8)
a)
No
b)
Yes
6.
Find all rational zeros
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
7.
If 2i is a zero, then
a)
2i repeats twice
b)
-2i is a zero too
c)
1-2i is a zero too
d)
0+2i is a zero too
8.
Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.
a)
A
b)
B
c)
C
d)
D
9.
Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.
a)
A
b)
B
c)
C
d)
D
10.
Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.
a)
A
b)
B
c)
C
d)
D
11.
Find all zeros.
a)
x= 3,1,1/3
b)
x= -3, -1, -1/3
c)
x = -3, 1, 1/3
d)
x = 3, -1, -1/3
12.
Find all the zeros of the polynomial.
a)
A
b)
B
c)
C
d)
D
13.
Find the zeros of the polynomial.
a)
A
b)
B
c)
C
d)
D
14.
Consider the polynomial function: P(x)=x4+18x3+a2-65x+63 where a is an unknown real number. If (x+9) is a factor of this polynomial, what is the value of a?
a)
21
b)
73
c)
63
d)
-31
15.
The volume of a rectangular prism is represented by the expression a3+4a2-3a-18. If the length is (a-2) and the height and width are equal, what is the width of the prism?
a)
a+3
b)
a-3
c)
a+2
d)
a-2
16.
The volume of a rectangular prism is represented by the expression a3+5a2-25a-125. If the length is (a-5) and the height and width are equal, what is the width of the prism?
a)
a-5
b)
a+5
c)
a+10
d)
a-10
17.
The volume of a rectangular prism is represented by the expression x3-17x2+96x-180. If the length is (x-5) and the height and width are equal, what is the width of the prism?
a)
(x+6)
b)
(x-6)
c)
(x-1)
d)
(x+1)
18.
Suppose p(x)=x3-2x2-33+k and that (x-6) is a factor. What is the value of k?
a)
-54
b)
-33
c)
33
d)
54
19.
Suppose p(x)=x3+16x2+56x+k and that (x+9) is a factor. What is the value of k?
a)
63
b)
-63
c)
81
d)
-81
20.
Let p(n)=n3+2n2-23n+k. If you divide p(n) by (n+6), the remainder is -1. What is the remainder if you divide p(n) by (n-5)?
a)
65
b)
1
c)
12
d)
55
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