Practice Exam Answers

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If f of negative 5 is equal to 0 , what are all the factors of the function f of x is equal to x cubed minus 19 x plus 30 ? Use the Remainder Theorem.

A
open paren x plus 2 close paren times open paren x minus 5 close paren times open paren x plus 3 close paren
B
open paren x minus 2 close paren times open paren x plus 5 close paren
C
open paren x minus 2 close paren times open paren x plus 5 close paren times open paren x minus 3 close paren
D
open paren x plus 2 close paren times open paren x minus 5 close paren
3

What is the sum of 12 minus 5 i and negative 3 plus 4 i ?

A
9 minus i
B
15 minus 9 i
C
negative 16 plus 63 i
D
9 minus 9 i
4

Solve for x in the equation x squared plus 11 x plus 121 fourths is equal to 125 fourths

A
x is equal to negative 11 plus or minus 25 halves
B
x is equal to negative 11 halves plus or minus the fraction with numerator 5 square root of 5 and denominator 2
C
x is equal to negative 11 halves plus or minus 25 halves
D
x is equal to negative 11 plus or minus the fraction with numerator 5 square root of 5 and denominator 2
5

Which second degree polynomial function has a leading coefficient of 2 and roots negative 3 and 5 ?

A
f of x is equal to 2 x squared minus 4 x minus 30
B
f of x is equal to 2 x squared minus 2 x minus 15
C
f of x is equal to 2 x squared plus 4 x minus 30
D
f of x is equal to 2 x squared plus 2 x minus 15
10

One root of a third degree polynomial function f of x is negative 5 plus 2 i Which statement describes the number and nature of all roots for this function?

A
f of x has three imaginary roots.
B
f of x has two real roots and one imaginary root.
C
f of x has three real roots.
D
f of x has two imaginary roots and one real root.
11

Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?

A
The pool must have been empty for the entire interval.
B
The pool must have been deeper at the end of the interval than it was at the start of the interval.
C
The pool must have been the same depth at the start of the interval as it was at the end of the interval.
D
The pool must have been more shallow at the end of the interval than it was at the start of the interval.
13

Which statement about 4 x squared plus 19 x minus 5 is true?

A
One of the factors is open paren 4 x minus 5 close paren .
B
One of the factors is open paren 4 x plus 1 close paren .
C
One of the factors is open paren x plus 5 close paren .
D
One of the factors is open paren x minus 4 close paren .
14

Which equation represents a graph with a vertex at open paren 1 comma negative 6 close paren ?

A
y is equal to 3 x squared minus 3 x minus 6
B
y is equal to 3 x squared minus 6 x minus 3
C
y is equal to 3 x squared plus 6 x minus 3
D
y is equal to 3 x squared minus 8 x minus 1
15

You can use a system of equations to graph and solve the polynomial equation 3 x cubed plus x is equal to 2 x squared plus 1 Which statement is true?

A
The y -coordinates of the solutions to the system and the zeroes of the equation are not equal.
B
The system has one solution, and the equation has three zeroes.
C
The equation has one zero, and the system has three solutions.
D
The x -coordinates of the solutions to the system and the zeroes of the equation are not equal.
16

The volume of a rectangular prism is given by the formula cap v is equal to l w h , where l is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism? Expand Image

A
6 x cubed plus 27 x squared plus 54 x
B
18 x to the 4th power plus 117 x cubed plus 162 x squared
C
6 x cubed plus 39 x squared plus 54 x
D
2 x squared plus 13 x plus 18
18

The side length, s , of a cube is 3 x plus 2 y If cap v is equal to s cubed , what is the volume of the cube?

A
27 x cubed plus 18 x squared y plus 12 x y squared plus 2 y cubed
B
27 x cubed plus 54 x squared y plus 18 x y squared plus 2 y cubed
C
3 x cubed plus 18 x squared y plus 36 x y squared plus 8 y cubed
D
27 x cubed plus 54 x squared y plus 36 x y squared plus 8 y cubed
19

A polynomial function has a root of negative 6 with multiplicity 3 and a root of 2 with multiplicity 4 If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

A
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 1, passing through (5 comma 8), touches x axis at (2 comma 0), curves up and passes through y axis at (0 comma 2). It then moves up and curves down at (negative 3 point 5 comma 6), passes through x axis at (negative 6 comma 0) and moves to quadrant 3 passing through (negative 7 comma negative 8).
B
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn.It starts from quadrant 3 passing through (negative 8 comma negative 1 point 5), it touches x axis at (negative 6 comma 0) and moves down and curves up at (negative 0 point 5 comma negative 3). It then passes through x axis at (2 comma 0) and moves to quadrant 1 passing through (4 comma 8).
C
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. it starts from quadrant 2 passing through (negative 8 comma 0 point 9), touches the x axis at (negative 6 comma 0), it curves up and passes through y axis at (0 comma 1 point 5). It then crosses x axis at (2 comma 0) moves to quadrant 4 through (5 comma negative 8).
D
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 2, passes through (negative 8 comma 8), crosses the x axis at (negative 6 comma 0), moves down and curves up at (negative 3 point 5 comma negative 3), and crosses the y axis at (0 comma negative 1). It then touches the x axis at (2 comma 0) and moves to quadrant 4 passing through (6 comma negative 8).

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