Question 1

Which of the following is the correct definition of a polynomial function of degree $$n$$?

Accepted Answer

$$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$$, where $$n is a $$nonnegative integer and $$a_n 
eq 0$

Question 2

Given the polynomial $$f(x) = 6x^4$ - 2x^3$ + 8x^2$ - 7$$, what is the leading coefficient?

Accepted Answer

$$6$$

Question 3

Which of the following functions is NOT a polynomial?

Accepted Answer

$$f(x) = x$$^{1/2}$$ + 4x$$

Question 4

What is the result when you subtract $$g(x) = 2x^2$ - 5x + 4$$ from $$f(x) = 3x^2$ + 9x - 2$$?

Accepted Answer

$$x^2 + 14x - 6$

Question 5

A chemical reaction produces a polynomial model for concentration over time: $$C(t) = 2t^3$ - 7t^2$ + 15t - 4. $$What is the degree of this polynomial?

Accepted Answer

$$3$$

Question 6

Which property is used to multiply polynomials such as $$(a+b)(c+d)$$?

Accepted Answer

Distributive Property

Question 7

Find the product: $$(2x^2 + 3x)(x - 2$$)$$

Accepted Answer

$$2x^3$$ - $$4x^2$$ + $$3x^2 - 6x$

Question 8

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

Accepted Answer

$$3x^2 - 4x + 3$

Question 9

A medical researcher models the growth of bacteria with $$B(t) = t^3$ - 2t^2$ + 5t - 7. If$$ $$t=2$$, what is the value of $$B(t)$$?

Accepted Answer

$$1$$

Question 10

Which of the following is a linear factor of $$f(x) = x^3$ + 2x^2$ - 5x - 35 if$$ $$x = -1 is a $$root?

Accepted Answer

$$(x+1)$$

Question 11

Factor the polynomial $$x^2 - 25$ completely.

Accepted Answer

$$(x-5)(x+5)$$

Question 12

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

Accepted Answer

Multiply all terms by zero

Question 13

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

Accepted Answer

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

Question 14

A business models profit with $$P(x) = 2x^2$ - 5x + 3. $$What is the sum of the coefficients?

Accepted Answer

$$0$$

Question 15

Which of the following is the remainder when $$x^2 - 7x + 15$ is divided by x-2$?

Accepted Answer

$$1$$

Question 16

If $$f(x) = x^2$ + 2x + 1$$, which of the following is true about its graph?

Accepted Answer

It is a parabola opening upwards with vertex at $$(-1, 0)$$

Question 17

Which of the following is the correct result of $$(x-4)(x+9)$$?

Accepted Answer

$$x^2 + 5x - 36$

Question 18

Which of the following is NOT a polynomial?

Accepted Answer

$$f(x) = x$$^{-2}$$ + 4x$$

Question 19

Which of the following is the correct factorization of $$x^2 + 9$ over the real numbers?

Accepted Answer

Cannot be factored over the real numbers

D1

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