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Polynomials — Test Answers

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Which simplified expression represents the area of the parallelogram?

A
negative 4 x cubed plus 14 x minus 24 square centimeters
B
negative 4 x cubed minus 14 x plus 24 square centimeters
C
2 x cubed minus 6 x squared minus 14 x plus 24 square centimeters
D
2 x cubed plus 6 x squared plus 14 x plus 24 square centimeters
2
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Let A , b , and c be real numbers where A is not equal to b is not equal to c is not equal to 0 Which of the following functions could represent the graph?

A
f of x is equal to open paren x minus A close paren squared times open paren x minus b close paren times open paren x minus c close paren to the 6th power
B
f of x is equal to x squared open paren x minus A close paren squared open paren x minus b close paren to the 4th power open paren x minus c close paren
C
f of x is equal to x to the 4th power open paren x minus A close paren open paren x minus b close paren cubed open paren x minus c close paren cubed
D
f of x is equal to x cubed open paren x minus A close paren cubed open paren x minus b close paren open paren x minus c close paren squared
3

Which product should Tomas choose?

A
open paren 2 x plus y close paren times open paren 4 x squared minus 2 x y plus y squared close paren
B
open paren 2 x plus y close paren times open paren 2 x squared minus 2 x y plus y squared close paren
C
open paren 2 x plus y close paren times open paren 4 x squared plus 2 x y minus y squared close paren
D
open paren 2 x plus y close paren times open paren 2 x squared plus 2 x y minus y squared close paren
4

Which is a potential rational root of f of x at point cap p ?

A
The root at point cap p may be 1 third .
B
The root at point cap p may be 5 thirds .
C
The root at point cap p may be 1 fifth .
D
The root at point cap p may be 3 fifths .
5

What is the completely factored form of x squared minus 16 x y plus 64 y squared ?

A
open paren x plus 8 y close paren times open paren x plus 8 y close paren
B
x y open paren x minus 16 plus 64 y close paren
C
open paren x minus 8 y close paren times open paren x minus 8 y close paren
D
x y open paren x plus 16 plus 64 y close paren
6

According to the Rational Root Theorem, which is a factor of the polynomial f of x is equal to 3 x cubed minus 5 x squared minus 12 x plus 20 ?

A
3 x minus 5
B
2 x minus 1
C
3 x plus 5
D
2 x plus 1
7

Which polynomial function has a leading coefficient of 2 , root negative 4 with multiplicity 3 , and root 10 with multiplicity 1 ?

A
f of x is equal to 3 open paren x plus 4 close paren open paren x plus 4 close paren open paren x minus 10 close paren
B
f of x is equal to 2 open paren x minus 4 close paren open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren
C
f of x is equal to 2 open paren x plus 4 close paren open paren x plus 4 close paren open paren x plus 4 close paren open paren x minus 10 close paren
D
f of x is equal to 3 open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren
8

Three roots of a fifth degree polynomial function f of x are negative 2 , 2 , and 4 plus i Which statement describes the number and nature of all roots for this function?

A
f of x has five real roots.
B
f of x has three real roots.
C
f of x has two real roots and one imaginary root.
D
f of x has three real roots and two imaginary roots.
9

The price that a company charged for a basketball hoop is given by the equation 50 minus 5 x squared where x is the number of hoops that are produced, in millions. It costs the company 30 dollars to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

A
1 point 4 million hoops
B
15 million hoops
C
30 million hoops
D
1 point 3 million hoops
10

What is the product of open paren 2 p plus 7 close paren times open paren 3 p squared plus 4 p minus 3 close paren ?

A
6 p cubed plus 29 p squared minus 22 p plus 21
B
6 p cubed plus 29 p squared plus 22 p minus 21
C
6 p cubed plus 29 p squared minus 34 p plus 21
D
6 p cubed plus 29 p squared plus 34 p minus 21
11

Use synthetic division to solve open paren x to the 4th power minus 1 close paren divided by open paren x minus 1 close paren What is the quotient?

A
x cubed minus x squared plus x minus 1
B
x cubed minus 2
C
x cubed plus x squared plus x plus 1
D
x cubed
12

According to the Rational Root Theorem, what are all the potential rational roots of f of x is equal to 5 x cubed minus 7 x plus 11 ?

A
plus or minus 1 fifth , plus or minus 1 , plus or minus 11 fifths , plus or minus 11
B
plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11
C
plus or minus 1 over 11 , plus or minus 5 over 11 , plus or minus 1 , plus or minus 5
D
0 , plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11
13

Which equation is quadratic in form?

A
5 x to the 6th power plus x to the 4th power plus 12 is equal to 0
B
6 x to the 4th power plus 7 x squared minus 3 is equal to 0
C
3 x to the 5th power plus 8 x cubed plus 6 is equal to 0
D
x to the 9th power plus x cubed minus 10 is equal to 0
14

Which statement best describes the equation open paren x plus 5 close paren squared plus 4 times open paren x plus 5 close paren plus 12 is equal to 0 ?

A
The equation is not quadratic in form because there is no real solution.
B
The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u is equal to open paren x plus 5 close paren .
C
The equation is not quadratic in form because it cannot be solved by using the quadratic formula.
D
The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.
15

Which of the following describes the roots of the polynomial function f of x is equal to open paren x plus 2 close paren squared times open paren x minus 4 close paren times open paren x plus 1 close paren cubed ?

A
2 with multiplicity 3 comma negative 4 with multiplicity 2 , and 1 with multiplicity 4
B
2 with multiplicity 2 comma negative 4 with multiplicity 1 , and 1 with multiplicity 3
C
negative 2 with multiplicity 3 comma 4 with multiplicity 2 comma and negative 1 with multiplicity 4
D
negative 2 with multiplicity 2 comma 4 with multiplicity 1 , and negative 1 with multiplicity 3
16

What is the quotient of open paren x cubed minus 3 x squared plus 3 x minus 2 close paren divided by open paren x squared minus x plus 1 close paren ?

A
x minus 2
B
x plus 1
C
x plus 2
D
x minus 4
17

Which polynomial function has a leading coefficient of 1 , roots negative 2 and 7 with multiplicity 1 , and root 5 with multiplicity 2 ?

A
f of x is equal to 2 open paren x plus 7 close paren open paren x plus 5 close paren open paren x minus 2 close paren
B
f of x is equal to 2 open paren x minus 7 close paren open paren x minus 5 close paren open paren x plus 2 close paren
C
f of x is equal to open paren x plus 7 close paren times open paren x plus 5 close paren times open paren x plus 5 close paren times open paren x minus 2 close paren
D
f of x is equal to open paren x minus 7 close paren times open paren x minus 5 close paren times open paren x minus 5 close paren times open paren x plus 2 close paren
18

Which statement about negative 2 h squared minus 15 h minus 7 is true?

A
One of the factors is open paren h plus 2 close paren .
B
One of the factors is open paren 3 h minus 2 close paren .
C
One of the factors is open paren h minus 7 close paren .
D
One of the factors is open paren 2 h plus 1 close paren .
19

Which table describes the behavior of the graph of f of x is equal to 2 x cubed minus 26 x minus 24 ?

A
Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 3 close paren'; Column 2, 'Above' Row 3: Column 1, 'open paren negative 3 comma negative 1 close paren'; Column 2, 'Below' Row 4: Column 1, '(−1, 4)'; Column 2, 'Above' Row 5: Column 1, '(4, ∞)'; Column 2, 'Below'
B
Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 4 close paren'; Column 2, 'Above' Row 3: Column 1, '(−4, 1)'; Column 2, 'Below' Row 4: Column 1, '(1, 3)'; Column 2, 'Above' Row 5: Column 1, '(3, ∞)'; Column 2, 'Below'
C
Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 4 close paren'; Column 2, 'Below' Row 3: Column 1, '(−4, 1)'; Column 2, 'Above' Row 4: Column 1, '(1, 3)'; Column 2, 'Below' Row 5: Column 1, '(3, ∞)'; Column 2, 'Above'
D
Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 3 close paren'; Column 2, 'Below' Row 3: Column 1, 'open paren negative 3 comma negative 1 close paren'; Column 2, 'Above' Row 4: Column 1, '(−1, 4)'; Column 2, 'Below' Row 5: Column 1, '(4, ∞)'; Column 2, 'Above'
20

What is the polynomial function of lowest degree with leading coefficient 1 and roots 1 and 1 plus i ?

A
f of x is equal to x squared minus 2 x plus 2
B
f of x is equal to x squared minus x plus 2
C
f of x is equal to x cubed minus x squared plus 4 x minus 2
D
f of x is equal to x cubed minus 3 x squared plus 4 x minus 2

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