MTH: 160 COLLEGE ALGEBRA
CHAPTER 4 Review
NAME_________________________
Please show all your work on this test
and place your final answers in the provided spaces.
Thank you and good luck.
1) See Worksheet Section 3.1 & 3.2
2)
List all possible rational zeros.
f (x) 
3)
1 3 1 2 1
1
x  x  x
5
3
6
10
Ans:_____________________________
Given that a polynomial has the given zeros:
7, - 7, 5 + 3i, 5 - 3i, -3.
Write the factors of the polynomial, but do not foil.
Ans:________________________________________________________________________
4)
Find the zeros of the polynomial function and state the multiplicity of each.
f ( x )  10  x  5 
3
 x  7
4
x5
Ans:_____________________________
1
5)
Use long division to find the quotient Q(x) and the remainder R(x), given:
a)
b)
P ( x )  2 x 3  12
Q( x ) : _____________________________
d(x)  x  2
R( x ) : _____________________________
P( x )  x 4  6x 2  5
Q( x ) : ______________________________
d(x)  x2  1
R( x ) : ______________________________
2
6)
Using synthetic division, state the quotient Q(x) and the remainder R(x) of the given
numbers. Decimal answers will not be accepted.
a)
-3, 2;
f ( x )  2x 3  5 x 2  x  6
Q( x ) : ______________________
R( X ) : ______________________
Q( x ) : _______________________
R( x ) : _______________________
b)
1
3
7
3, - ; f ( x )   x 3  x 2  x 
2
2
2
Q( x ) : _______________________
R( x ) : _______________________
Q( x ) : _______________________
R( x ) : _______________________
3
7)
Find a polynomial function of degree 3 with the given numbers as zeros: 5, 3i, -3i
Ans:__________________________
8)
Suppose that a polynomial function of degree 5 with rational coefficients has the given
numbers as zeros. What are the other zeros?
a)
7, 3 - 5i, 7 - 3
Ans:_______________________
b)
-7, 3i, -5i
Ans:_______________________
4
9)
Given the rational functions in part a) and b): state the following if they exist:
a)
f (x) 
x2
x  2 x  15
2
Domain : { x |
}
VA's:
HA:
Does graph cross HA?
If so, where?
X-intercept's :
Y-intercept :
b)
f (x) 
x2
x2  x  2
Domain : { x |
}
VA's:
HA:
Does graph cross HA?
If so, where?
X-intercept's :
Y-intercept :
5