Question 1

Which of the following is a trinomial?

Accepted Answer

$5x^2 + 2y - 7$

Question 2

Given the polynomial $f(x) = (x-2)^2(x+1)$, what is the multiplicity of the root at $x = 2$?

Accepted Answer

$2$

Question 3

If a polynomial $f(x)$ has a root at $x = 3$ with multiplicity 2, what does the graph do at $x = 3$?

Accepted Answer

It turns around and touches the x-axis.

Question 4

What is the result when $2x^3 - 3x^2 + 4x - 5$ is divided by $x - 2$ using synthetic division?

Accepted Answer

$2x^2 + x + 6$ remainder $-7$

Question 5

Which of the following best describes the process of long division of polynomials?

Accepted Answer

It is a process similar to integer division, producing a quotient and a remainder.

Question 6

Given $f(x) = (x+2)^3(x-1)^2$, how does the graph behave at $x = -2$?

Accepted Answer

It touches the x-axis and flattens out.

Question 7

What is the quotient when $3x^3 + 2x^2 - x + 5$ is divided by $x + 1$ using synthetic division?

Question 8

If $f(x) = x^3 - 4x^2 + 5x - 2$, and $x = 1$ is a root, what is the result of dividing $f(x)$ by $x - 1$?

Accepted Answer

$x^2 - 3x + 2$

Question 9

Which statement about the remainder in polynomial long division is correct?

Accepted Answer

The remainder has a degree less than the divisor.

Question 10

A polynomial $f(x)$ is divided by $x - 3$ and the remainder is $5$. What does this tell you about $f(3)$?

Accepted Answer

$f(3) = 5$

Question 11

Which of the following is NOT a property of synthetic division?

Accepted Answer

It can be used to divide by any polynomial.

Question 12

If $f(x) = x^4 - 2x^3 + x^2 - x + 2$ is divided by $x - 1$, what is the remainder?

Accepted Answer

$3$

Question 13

Which of the following best describes a binomial?

Accepted Answer

A polynomial with two terms.

Question 14

If $f(x) = (x-2)^2(x+3)$, which of the following statements is true?

Accepted Answer

The graph touches the x-axis at $x = 2$ and crosses at $x = -3$.

Question 15

What is the degree of the polynomial $5x^2 + 2y - 7$?

Accepted Answer

$2$

Question 16

Which of the following is the correct result of dividing $x^3 + 2x^2 - x + 4$ by $x + 2$ using synthetic division?

Accepted Answer

$x^2 + 0x - 1$ remainder $6$

Question 17

If a polynomial $f(x)$ has a root at $x = -1$ with multiplicity 3, what does the graph do at $x = -1$?

Accepted Answer

It crosses the x-axis and flattens out.

Polynomials: Roots, Long Division, and Synthetic Division

Study Guide - Practice Questions