Answers Mathematics IIIPolynomial Functions and Equations

Polynomial Functions and Equations — Test Answers

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What are the possible degrees for the polynomial function?

odd degrees of 5 or greater

even degrees of 6 or greater

degrees of 5 or greater

degrees of 6 or greater

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What are the roots of the polynomial equation x cubed minus 7 x is equal to 6 x minus 12 ? Use a graphing calculator and a system of equations.

negative 3 , negative 1 , 4

negative 6 , 6

negative 4 , 1 , 3

1 , 3

Which expression represents the sixth term in the binomial expansion of open paren 5 y plus 3 close paren to the 10th power ?

5 sub 10 cap c sub 6 y to the 4th power 3 to the 6th power

10 cap c sub 5 5 y to the 5th power 3 to the 5th power

10 cap c sub 6 5 y to the 4th power 3 to the 6th power

5 sub 10 cap c sub 5 y to the 5th power 3 to the 5th power

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

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'

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'

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'

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'

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 ?

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

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

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

plus or minus 1 over 11 , plus or minus 5 over 11 , plus or minus 1 , plus or minus 5

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

The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to 3 .

The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to negative 3 .

The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to negative 3 .

The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to 3 .

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

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

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

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

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

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 ?

3 x plus 5

2 x plus 1

2 x minus 1

3 x minus 5

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?

She is correct because all solutions are intersection points of the graphs.

She is incorrect because the solutions may have multiplicity greater than 1.

She is correct because the solutions are irrational.

She is incorrect because systems may have only complex solutions which are not visible on a graph.

Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. He sets the expressions equal to y and graphs the equations. What is the greatest possible number of intersections for these graphs?

none

two

infinitely many

one

Which statement describes how the graph of the given polynomial would change if the term negative 3 x to the 6th power is added? y is equal to 2 x to the 6th power plus 9 x to the 5th power minus 7 x cubed minus 1

Both ends of the graph will approach positive infinity.

The ends of the graph will extend in opposite directions.

The ends of the graph will approach zero.

Both ends of the graph will approach negative infinity.

Which graph can be used to find the solution(s) to 4 x is equal to negative 4 x ?

Image with description On a coordinate plane, the x and y axes ranges from negative 6 to 6 with an increment of 1 unit. One of the lines passes through point 4 comma 0 and 0 comma negative 4. The other line passes through point 0 comma 4 and negative 4 comma 0.

Image with description On a coordinate plane, the x and y axes ranges from negative 6 to 6 with an increment of 1 unit. There are two lines and both the lines are parallel to x-axis. One passes through point 0 comma negative 4 and the other line goes through point 0 comma 4.

Image with description On a coordinate plane, the x and y axes ranges from negative 6 to 6 with an increment of 1 unit. One of the lines passes through 4 comma 0 and 2 comma 2. The other line passes through negative 4 comma 0 and negative 2 comma 2.

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 6 to 6 with an interval of 1 unit. One of the lines passes through (1 comma 4) and (negative 1 comma negative 4). The other line goes through (1 comma negative 4) and (negative 1 comma 4).

What is the fifth term in the binomial expansion of open paren x plus 5 close paren to the 8th power ?

3 comma 125 x to the 5th power

7 comma 000 x to the 5th power

175 comma 000 x cubed

43 comma 750 x to the 4th power

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?

x cubed minus 2

x cubed minus x squared plus x minus 1

x cubed plus x squared plus x plus 1

x cubed

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 ?

2 with multiplicity 2 comma negative 4 with multiplicity 1 , and 1 with multiplicity 3

2 with multiplicity 3 comma negative 4 with multiplicity 2 , and 1 with multiplicity 4

negative 2 with multiplicity 2 comma 4 with multiplicity 1 , and negative 1 with multiplicity 3

negative 2 with multiplicity 3 comma 4 with multiplicity 2 comma and negative 1 with multiplicity 4

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

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

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

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

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

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.

open paren x plus 2 close paren times open paren x plus 60 close paren

open paren x minus 2 close paren times open paren x minus 60 close paren

open paren x minus 10 close paren times open paren x plus 2 close paren times open paren x plus 6 close paren

open paren x plus 10 close paren times open paren x minus 2 close paren times open paren x minus 6 close paren

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?

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).

Image with description On a coordinate plane, the x and y axes ranges from negative 8 to 8 with an increment of 1. The polynomial graph is drawn on the coordinate plane. The curve starts from quadrant III, 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. Here the curve moves up slightly and passes through the point 2 comma 0, goes down, curves up to the point 2 comma negative 2, crosses x axis once again at point 3 comma 0 and moves to quadrant IV through the point 3 point 5 comma negative 8.

Image with description On a coordinate plane, the x and y axes ranges from negative 8 to 8 with an increment of 1. The polynomial graph is drawn on the coordinate plane. The curve starts from negative 3 point 8 comma 8, touches the x axis at negative 3 comma 0, passes through the point negative 1 point 5 comma 3 point 5 and comes down to the origin. Here the curve goes down slightly and curves up to the point 2 point 1, curves down to touch x axis at point 2 comma 0 and moves to quadrant I through the point 4 comma 8.

Image with description On a coordinate plane, the x and y axes ranges from negative 8 to 8 with an increment of 1. The polynomial graph is drawn on the coordinate plane. It starts from quadrant I passing through the point negative 3 point 8 comma 8 crosses x axis at negative 3 comma 0, goes down and curves up at the point negative 2 comma negative 3 point 5, crosses the y axis at the point 0 comma negative 0 point 8. Here the curve touches the x axis at point 1 comma 0, goes down slightly and again crosses the x axis at point 3 comma 0, and moves to quadrant I through the point 4 comma 7.

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?

1 point 3 million hoops

1 point 4 million hoops

30 million hoops

15 million hoops

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

x cubed minus 6 x squared y plus 12 x y squared minus 8 y cubed

3 x cubed plus 6 x squared y plus 12 x y squared plus 24 y cubed

x cubed plus 6 x squared y plus 12 x y squared plus 8 y cubed

3 x cubed minus 6 x squared y plus 12 x y squared minus 24 y cubed

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