Free Practice Quiz Question List

02/10 — Polynomial Functions Online Quiz Questions

Use this free practice quiz with 20 questions to review 02/10 — Polynomial Functions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

What is the simplified result of $(3x^3-2x^2+5x-7)+(x^3+4x^2-2x+1)$ ?

A
$4x^3+6x^2+3x-8$
B
$2x^3+2x^2+7x-6$
C
$4x^3+2x^2+3x-6$
D
$4x^3-6x^2+7x-8$

True or false

1 point

Every polynomial function is continuous and has no vertical asymptotes.

A
True
B
False

Written response

1 point

What is the degree of the product $(x^3-1)(2x^5+x)$ ?

Fill in the blank

1 point

Complete the polynomial Division Algorithm: if f(x) is divided by a nonzero polynomial d(x), then f(x) = , where the remainder is zero or has degree less than the divisor.

Choose one

1 point

What is the end behavior of $g(x)=-2x^5+x^2-7$ ?

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

True or false

1 point

A polynomial of degree n can have no more than n - 1 turning points.

A
True
B
False

Written response

1 point

What theorem states that the remainder when a polynomial f(x) is divided by x-c equals f(c)?

Choose all

1 point

A polynomial with real coefficients has zero 3 - 2i. Select all conclusions that must follow.

A
3 + 2i is also a zero.
B
3 - 2i is not a zero.
C
x^2 - 6x + 13 is a real quadratic factor.
D
x^2 + 6x + 13 is the corresponding real quadratic factor.

Fill in the blank

1 point

Complete the Factor Theorem: f(c) = if and only if is a factor of f(x).

Choose all

1 point

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

A
The polynomial has degree 5.
B
The graph touches the x-axis at x=-2 and turns around.
C
The graph touches the x-axis at x=1 and turns around.
D
The graph passes through (0,4).

Choose one

1 point

Which value is not a possible rational zero of $2x^3-3x^2-8x+12$ according to the Rational Zero Theorem?

A
1/2
B
3/2
C
5/2
D
3

Written response

1 point

For $f(x)=2x^3-3x^2-8x+12$ , what is f(1)?

Open ended

1 point

Divide $x^3+2x^2-x-2$ by x-1. State the quotient and remainder, factor the quotient completely, and identify all zeros of the polynomial.

Choose one

1 point

For the polynomial $p(x)=-4x^5+7x^3-x+9$ , which statement correctly identifies its degree and leading coefficient?

A
The degree is 4, and the leading coefficient is -4.
B
The degree is 5, and the leading coefficient is -4.
C
The degree is 5, and the leading coefficient is 4.
D
The degree is -4, and the leading coefficient is 5.

True or false

1 point

True or false: The Rational Zero Theorem guarantees that every number it lists is a zero of the polynomial.

A
True
B
False

Choose one

1 point

Simplify $(2x^3-5x+4)+(x^3+2x-7)$ .

A
$3x^3-7x+11$
B
$x^3-3x-3$
C
$3x^3-3x-3$
D
$3x^6-3x-3$

Written response

1 point

Given $f(x)=3x^2-2x+1$ , enter the value of $f(-1)$ .

Choose one

1 point

Simplify the product $(3x+4)(3x-4)$ .

A
$9x^2-16$
B
$9x^2+16$
C
$6x^2-16$
D
$3x^2-4$

Choose one

1 point

Which number should be used in synthetic division when dividing a polynomial by $x+3$ ?

A
3
B
-1
C
0
D
-3

Choose one

1 point

What is the end behavior of $f(x)=2x^5-3x^2+1$ ?

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