Practice Test, 3.5-4.2, Part 2
Question: 13
Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,
determine p( k ) .
p( x ) = 8x4 - 29x3 - 6x2 + 72x - 27; k = 3
Is k a zero of this polynomial?
Yes No
Question: 14
Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,
determine p( k ) .
p( x ) = 4x3 - x2 - 10x - 8; k = 2
Is k a zero of this polynomial?
Yes No
Question: 15
Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,
determine p( k ) .
p( x ) = 4x2 - ( 5 - 7i )x + ( 36 - 20i ); k = -4i
Is k a zero of this polynomial?
Yes No
Question: 16
Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,
determine p( k ) .
p( x ) = 2x5 - 6x4 + 2x3 - 8x2 + 7x + 3; k = 2
Is k a zero of this polynomial?
Yes
No
Question: 17
r( x )
d( x ) ,
where d( x ) is the denominator of the original fraction, q( x ) is the quotient, and
r( x ) is the remainder.
x3 + x2 - 7x - 14
x - 1
Use synthetic division to rewrite the following fraction in the form q( x ) +
Question: 18
r( x )
d( x ) ,
where d( x ) is the denominator of the original fraction, q( x ) is the quotient, and
r( x ) is the remainder.
2x5 - 12x4 + 24x3 - 28x2 - 16x
x - 4
Use synthetic division to rewrite the following fraction in the form q( x ) +
Question: 19
r( x )
d( x ) ,
where d( x ) is the denominator of the original fraction, q( x ) is the quotient, and
r( x ) is the remainder.
2x4 + ( 4 - 2i )x3 - ( 5 + 4i )x2 + 5ix
x - i
Use synthetic division to rewrite the following fraction in the form q( x ) +
Question: 20
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of - 3, - 2, and 5, and a y -intercept of - 9.
Answer:
f(x)=
Question: 21
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Second-degree, with zeros of - 2 and 1, and goes to -Ù as x ® -Ù.
Answer:
f(x)=
Question: 22
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Fourth-degree and a single x -intercept of 2.
Answer:
f(x)=
Question: 23
Describe the left and right tendencies and sketch the graphs for each of the following:
P(x) = 2x4 – 3x3 –6x2 –x – 23
F(x) = (x – 3)(2x + 1)(x + 5)
2