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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