Free Practice Quiz Question List

08/14 8. Higher-Degree Polynomial Functions Online Quiz Questions

Use this free practice quiz with 20 questions to review 08/14 8. Higher-Degree Polynomial Functions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

A polynomial $f(x)$ satisfies $f(2)=0$ . Which expression must be a factor of $f(x)$ ?

A
$x-2$
B
$x+2$
C
$2x-1$
D
$2x+1$

Choose one

1 point

What is the end behavior of a polynomial with odd degree and a negative leading coefficient?

A
The left end falls and the right end rises.
B
Both ends rise.
C
The left end rises and the right end falls.
D
Both ends fall.

Choose one

1 point

Which interval notation represents the solution set of $x^3-x^2-4x+4\ge 0$ ?

A
$(-\infty,-2)\cup(1,2)$
B
$[-2,1]\cup[2,\infty)$
C
$(-\infty,-2]\cup[1,2]$
D
$[-2,2]$

Choose all

1 point

Select all conditions guaranteed by the Rational Root Theorem for a rational zero $\frac{p}{q}$ written in lowest terms for a polynomial with integer coefficients.

A
$p$ divides the constant term.
B
$p$ divides the leading coefficient.
C
$q$ divides the leading coefficient.
D
$q$ must equal $1$ .

Choose all

1 point

For $f(x)=(x-1)^2(x+3)^3$ , select all statements that are correct.

A
The graph touches the x-axis at $x=1$ .
B
The graph crosses the x-axis at $x=-3$ .
C
The graph has degree $4$ .
D
The graph falls to the left and rises to the right.

True or false

1 point

Every polynomial function is continuous, so its graph has no holes or vertical asymptotes.

A
True
B
False

True or false

1 point

If $2+3i$ is a zero of a polynomial with real coefficients, then $2-3i$ must also be a zero.

A
True
B
False

Written response

1 point

For $f(x)=-2(x+1)^2(x-3)$ , what is the y-intercept value?

Written response

1 point

How many complex zeros does a fourth-degree polynomial have when repeated zeros are counted?

Fill in the blank

1 point

Complete the factorization: $x^3-4x^2-x+4=$ .

Fill in the blank

1 point

For $f(x)=(x-2)^2(x+1)$ , crossing $x=2$ does not the sign of the polynomial, while crossing $x=-1$ the sign.

Choose one

1 point

What is the value of $(3+2i)(3-2i)$ ?

A
$5$
B
$13$
C
$9$
D
$17$

Choose one

1 point

A polynomial has odd degree and a negative leading coefficient. Which end behavior must its graph have?

A
The left end falls and the right end rises.
B
The left end rises and the right end falls.
C
Both ends rise.
D
Both ends fall.

True or false

1 point

True or false: Every fourth-degree polynomial has four distinct complex zeros.

A
True
B
False

Choose one

1 point

A polynomial with real coefficients has $2+3i$ as a zero. Which number must also be a zero?

A
$2+3i$
B
$-2+3i$
C
$2-3i$
D
$-2-3i$

Choose one

1 point

Which value is a possible rational zero of $f(x)=2x^3-3x^2-8x+12$ according to the Rational Root Theorem?

A
$\frac{5}{2}$
B
$\frac{3}{2}$
C
$\frac{7}{3}$
D
$\frac{5}{4}$

Written response

1 point

What theorem states that $f(k)=0$ if and only if $(x-k)$ is a factor of $f(x)$ ?

Choose one

1 point

For $f(x)=-2(x+1)^2(x-3)$ , what happens at the zero $x=-1$ ?

A
The graph touches the x-axis and turns around.
B
The graph crosses the x-axis.
C
The graph has a vertical asymptote.
D
The graph has no x-intercept.

Open ended

1 point

A rectangular box has dimensions $x$ , $x+1$ , and $x+2$ units, and its volume is $60$ cubic units. Solve for $x$ , reject solutions that are not valid dimensions, and state all three dimensions. Show how the polynomial equation is formed and solved.

Written response

1 point

Simplify $(2+3i)+(4-7i)$ and enter the result in standard form.