AnswersAlgebra IIPolynomial Functions

Polynomial Functions — Test Answers

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1
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What are the roots of the polynomial equation?

A
negative 3 , negative 2 , 3
B
negative 3 , 2
C
18 , 32 , 66
D
18 , 32
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 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
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 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
3

What are the solutions of the equation open paren x minus 3 close paren squared plus 2 times open paren x minus 3 close paren minus 8 is equal to 0 ? Use u substitution to solve.

A
x is equal to 1 and x is equal to 7
B
x is equal to negative 1 and x is equal to negative 7
C
x is equal to negative 1 and x is equal to 5
D
x is equal to negative 5 and x is equal to 1
4

Which equation is quadratic in form?

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

A polynomial function has a root of negative 3 with multiplicity 2 , a root of 0 with multiplicity 1 , a root of 1 with multiplicity 1 , and a root of 3 with multiplicity 2 If the function has a positive leading coefficient and is of even 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(negative 3 point 8 comma 8) crosses x axis at (negative 3 comma 0), goes down and curves up at (negative 2 comma negative 3 point 5), crosses the y axis at (0 comma negative 0 point 8). From here it touches the x axis at (1 comma 0), goes down slightly and again crosses the x axis at (3 comma 0), and moves to quadrant 1 through the point (4 comma 7).
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 the point (negative 3 point 5 comma negative 8), touches the x axis at (3 comma 0), moves down and curves up at (negative 1 point 8 comma 7), and passes through the origin. From here it moves up slightly and passes through (2 comma 0), goes down, curves up at (2 comma negative 2), crosses x axis once again at (3 comma 0) and moves to quadrant 4 through the point (3 point 5 comma negative 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. The graph starts from quadrant 3 passing through the point (negative 3 point 5 comma negative 8), it crosses the x axis at (negative 3 comma 0) moves up and curves down at (negative 2 comma 7), crosses the y axis at (0 comma 1), crosses the x axis at (1 comma 0), moves up and curves down at (2 point 5 comma 1). It then moves down, crosses x axis at (2 comma 0) and moves to quadrant 4 through the point (4 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 (negative 3 point 8 comma 8), touches the x axis at (negative 3 comma 0), goes up to (negative 1 point 5 comma 3 point 5) and comes down to the origin. From here it goes down slightly and curves up to (2 point 1), curves down to touch x axis at (2 comma 0) and moves to quadrant 1 through the point (4 comma 8).
6

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 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
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 3 open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren
D
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
7

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 two real roots and one imaginary root.
B
f of x has three real roots.
C
f of x has three real roots and two imaginary roots.
D
f of x has five real roots.
8

Which statement describes the graph of this polynomial function? f of x is equal to x to the 5th power minus 6 x to the 4th power plus 9 x cubed

A
The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to negative 3 .
B
The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to 3 .
C
The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to 3 .
D
The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to negative 3 .
10

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
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
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
plus or minus 1 fifth , plus or minus 1 , plus or minus 11 fifths , plus or minus 11
12

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 cubed minus 3 x squared plus 4 x minus 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 squared minus x plus 2
13

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 2
B
x cubed plus x squared plus x plus 1
C
x cubed minus x squared plus x minus 1
D
x cubed
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 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 .
B
The equation is not quadratic in form because there is no real solution.
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

What is the completely factored form of f of x is equal to 6 x cubed minus 13 x squared minus 4 x plus 15 ?

A
open paren x plus 1 close paren squared times open paren 2 x minus 3 close paren
B
open paren x plus 1 close paren times open paren 2 x minus 3 close paren times open paren 3 x minus 5 close paren
C
open paren x plus 1 close paren times open paren 6 x squared minus 19 x plus 15 close paren
D
open paren x plus 1 close paren times open paren 3 x minus 2 close paren times open paren 5 x minus 3 close paren
16

If f of negative 2 is equal to 0 , what are all the factors of the function f of x is equal to x cubed minus 2 x squared minus 68 x minus 120 ? Use the Remainder Theorem.

A
open paren x minus 10 close paren times open paren x plus 2 close paren times open paren x plus 6 close paren
B
open paren x plus 2 close paren times open paren x plus 60 close paren
C
open paren x minus 2 close paren times open paren x minus 60 close paren
D
open paren x plus 10 close paren times open paren x minus 2 close paren times open paren x minus 6 close paren
18

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

A
She is incorrect because the solutions may have multiplicity greater than 1.
B
She is correct because the solutions are irrational.
C
She is correct because all solutions are intersection points of the graphs.
D
She is incorrect because systems may have only complex solutions which are not visible on a graph.
19

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 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
B
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
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 2 open paren x minus 7 close paren open paren x minus 5 close paren open paren x plus 2 close paren
20

Which geometric series converges?

A
1 over 81 plus 1 over 27 plus 1 ninth plus 1 third plus dot dot dot
B
the sum from n is equal to 1 to infinity of 7
C
the sum from n is equal to 1 to infinity of 1 fifth
D
1 plus 1 half plus 1 fourth plus 1 eighth plus dot dot dot

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