$$2x^2 - x - 1$ \,\text{remainder}\, -6$

$$3x + 1$$ \,\text{remainder}\, 4$

Question 1

Which of the following is the leading coefficient of the polynomial $$f(x) = 6x^4$ - 2x^3$ + 8x - 5$$?

Accepted Answer

$$6$$

Question 2

Given the polynomial $$f(x) = x^3$ - 2x^2$ - 5x + 6$$, which of the following is a linear factor of $$f(x)$$?

Accepted Answer

$$(x-1)$$

Question 3

Which of the following expressions is NOT a polynomial function?

Accepted Answer

$$f(x) = x$$^{1.5}$$ + 2x$$

Question 4

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

Accepted Answer

$$2x^2 - x - 1$ \,	ext{remainder}\, -6$

Question 5

Which of the following best describes the degree and leading term of the polynomial $$f(x) = 4x^5$ - 7x^3$ + 2x$$?

Accepted Answer

Degree: $$5$$, Leading term: $$4x^5$$

Question 6

If $$x-3 is a $$factor of $$f(x) = x^3$ - 2x^2$ - 5x + 6$$, what is the value of $$f(3)$$?

Accepted Answer

$$0$$

Question 7

Which of the following is the correct factorization of $$2x^2 - 5x - 3$?

Accepted Answer

$$(2x+1)(x-3)$$

Question 8

A company models its profit with the polynomial $$P(x) = x^3$ - 4x^2$ + 4x. $$What is the sum of the coefficients?

Accepted Answer

$$0$$

Question 9

Which of the following is the result of multiplying $$(x-4)(x+2)$$?

Accepted Answer

$$x^2 - 2x - 8$

Question 10

Divide $$18 - 24x + 42x^2$ by 6x$. What is the quotient?

Accepted Answer

$$3x - 4 + 7/x$$

Question 11

Which of the following is a correct application of the distributive property to $$a(b + c)$$?

Accepted Answer

$$ab + ac$$

Question 12

Given $$f(x) = x^2$ - 4$$, which of the following is a correct factorization?

Accepted Answer

$$(x-2)(x+2)$$

Question 13

Which of the following is the correct sum of $$2x^2 + 3x - 1$ and 4x^2$ - x + 5$$?

Accepted Answer

$$6x^2 + 2x + 4$

Question 14

Which of the following is NOT a valid strategy for factoring polynomials?

Accepted Answer

Multiply all terms by zero.

Question 15

If $$f(x) = x^3$ + 2x^2$ - 5x - 6$$ and $$x+3 is a $$factor, which of the following is also a factor?

Accepted Answer

$$(x-1)$$

Question 16

Which of the following best describes the polynomial $$f(x) = 5x^4$ + 2x^2$ - 7$$?

Accepted Answer

Quartic trinomial

Question 17

A rectangular garden has an area modeled by $$A(x) = x^2$ + 5x + 6. $$What are the possible dimensions of the garden?

Accepted Answer

$$(x+2)$$ and $$(x+3)$$

Question 18

Which of the following is the correct result of subtracting $$3x^2 - x + 4$ from 5x^2$ + 2x - 1$$?

Accepted Answer

$$2x^2 + 3x - 5$

Question 19

Which of the following is the quotient and remainder when $$3x^2 - 5x + 2$ is divided by x-2$?

Accepted Answer

$$3x + 1$$ \,	ext{remainder}\, 4$

D1

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