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?

Accepted Answer

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

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