Free Practice Quiz Question List

06/14 6. Polynomial Expressions and Functions Online Quiz Questions

Use this free practice quiz with 20 questions to review 06/14 6. Polynomial Expressions and Functions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

What is the leading coefficient of $f(x)=-7x^4+3x^2-x+9$ ?

A
7
B
-7
C
3
D
9

Written response

1 point

What is the degree of $p(x)=4x^7-2x^3+x-6$ ?

Choose all

1 point

Select all statements that correctly describe the Polynomial Division Algorithm.

A
The divisor must be nonzero.
B
The equation $f(x)=d(x)q(x)+r(x)$ holds.
C
The degree of the remainder is less than the degree of the divisor.
D
The remainder is always a constant.

Fill in the blank

1 point

Complete the identity: $(a-b)^2=$ .

Choose one

1 point

Simplify $(5x^2-3x+4)-(2x^2+x-6)$ .

A
$3x^2-2x-2$
B
$7x^2-4x-2$
C
$3x^2-4x+10$
D
$7x^2-2x+10$

Choose all

1 point

For the polynomial $f(x)=2x^3-3x^2-8x+12$ , select all values that could be rational zeros according to the Rational Zero Theorem.

A
$1$
B
$-1$
C
$\frac{3}{2}$
D
$-\frac{3}{2}$
E
$\frac{5}{2}$

Fill in the blank

1 point

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

Written response

1 point

What is the remainder when $f(x)=x^3+2x^2-5x+1$ is divided by $x-2$ ?

Choose one

1 point

Which factorization is correct for $16x^2-81$ ?

A
$(4x-9)(4x+9)$
B
$(4x-9)^2$
C
$(16x-9)(x+9)$
D
$(4x-81)(4x+1)$

Open ended

1 point

Factor $f(x)=x^3-4x^2-x+4$ completely and state all of its zeros. Show the main factoring steps and explain how the factors determine the zeros.

Choose one

1 point

Which expression is not a polynomial?

A
$3x^2-5x+1$
B
$x^{\frac{1}{2}}+4$
C
$-7x^4+2$
D
$9$

True or false

1 point

True or false: The polynomial $f(x)=x^2+4$ has no real zeros but has two complex zeros when multiplicities are counted.

A
True
B
False

Choose one

1 point

Simplify $(2x^3-4x+6)+(5x^3-3x+1)$ .

A
$7x^3-7x+7$
B
$7x^3+x+5$
C
$3x^3-7x+7$
D
$7x^6-7x+7$

Written response

1 point

What is the remainder when $f(x)=x^3-3x^2+x-1$ is divided by $x-2$ ?

Choose one

1 point

When $x^3+x^2+x+1$ is divided by $x-1$ , which quotient and remainder result?

A
$x^2+2x+3$ , remainder $-4$
B
$x^2-2x+3$ , remainder $4$
C
$x^2+2x+3$ , remainder $4$
D
$x^2+x+3$ , remainder $4$

Choose one

1 point

Suppose $f(3)=0$ . Which statement correctly applies a theorem to identify a factor of $f(x)$ ?

A
The Remainder Theorem; $x+3$ is a factor.
B
The Factor Theorem; $x-3$ is a factor.
C
The Rational Zero Theorem; $x-3$ is a factor.
D
The Factor Theorem; $x+3$ is a factor.

Written response

1 point

What theorem states that if $f(5)=0$ , then $x-5$ is a factor of $f(x)$ ?

Choose one

1 point

Which factorization is correct for $9x^2-16$ ?

A
$(3x-4)(3x+4)$
B
$(3x-8)(3x+2)$
C
$(9x-4)(x+4)$
D
$(3x-4)^2$

True or false

1 point

True or false: For $f(x)=2x^3-5x^2-4x+3$ , the Rational Zero Theorem identifies $\frac{3}{2}$ as a possible rational zero.

A
True
B
False

True or false

1 point

True or false: For $f(x)=(x-1)^4(x+2)^3$ , the graph generally touches the $x$ -axis at $x=1$ and crosses the $x$ -axis at $x=-2$ .

A
True
B
False