Question 1

Which of the following expressions is NOT a polynomial?

Accepted Answer

$$\dfrac{2x}{x-5}$$

Question 2

What is the degree of the polynomial $$10x^3$$ - $$5x^2 + 4x + 22$?

Accepted Answer

$$3$$

Question 3

A chemist is mixing two solutions. The concentration of the first is modeled by $$3x^2 + 2x$, and the second by 5x^2$ - x + 4. $$What is the sum of the concentrations, in standard form?

Accepted Answer

$$8x^2 + x + 4$

Question 4

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 5

A rectangular garden has a length of $$2x + 3$$ meters and a width of $$x - 2$$ meters. What is the area of the garden, expressed as a polynomial in standard form?

Accepted Answer

$$2x^2 - x - 6$

Question 6

Simplify the rational expression: $$\dfrac{x^2$ - 9}{x^2$ - 6x + 9}$$

Accepted Answer

$$\dfrac{x + 3}{x - 3}$$

Question 7

Find all real numbers that must be excluded from the domain of $$\dfrac{3x}{x^2$ - 25}.$$

Accepted Answer

$$x = 5, x = -5$$

Question 8

A company’s profit, in thousands of dollars, is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$

Question 9

Which of the following trinomials is prime (cannot be factored over the integers)?

Accepted Answer

$$x^2 + 2x + 7$

Question 10

Subtract the polynomials: $$(4x^2 + 2x - 5$$) - $$(x^2 - 3x + 7$$)$$

Accepted Answer

$$3x^2 + 5x - 12$

Question 11

A projectile is launched from the ground and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t. $$What is the maximum height reached by the projectile?

Accepted Answer

$$40.8$$ meters

Question 12

Which of the following is the product of $$(x + 4)(x - 7)$$?

Accepted Answer

$$x^2 - 3x - 28$

Question 13

Simplify the rational expression: $$\dfrac{2x^2$ + 8x}{4x}$$

Accepted Answer

$$\dfrac{x + 4}{2}$$

Question 14

Add the rational expressions: $$\dfrac{3}{x} + \dfrac{2}{x^2$}$$

Accepted Answer

$$\dfrac{3x + 2}{x^2$}$$

Question 15

Given the graph of $$y = x^2$ + 4$$, what is the y-intercept?

Accepted Answer

$$4$$

Question 16

If $$f(x) = x^2$ - 4x + 3$$, what are the x-intercepts of the function?

Accepted Answer

$$x = 3$$ and $$x = 1$$

Question 17

A rectangle has a length of $$x + 2$$ and a width of $$x - 2. $$What is the area of the rectangle?

Accepted Answer

$$x^2 - 4$

Question 18

Which of the following is the correct factorization of $$x^2 + 5x + 6$?

Accepted Answer

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

Question 19

If $$g(x) = 2x^2$ - 8x + 6$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -2)$$

College Algebra: Polynomials, Rational Expressions, and Graphing Study Guide

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