Question 1

Simplify the following expression and write your answer in standard form: $$\left(5 + 3i\right)\left(9 - i\right).$$

Accepted Answer

$$48 + 22i$$

Question 2

Evaluate $$\dfrac{2x - 5}{x + 5}$$ for $$x = 3 + i.$$

Accepted Answer

$$-2 + i$$

Question 3

Solve for $$x$$: $$8x^2 + 4x = 2$.

Accepted Answer

$$x = \dfrac{-1 \pm \sqrt{5}}{4}$$

Question 4

Find the vertex of the quadratic function $$f(x) = 4x^2$ + 5x - 9.$$

Accepted Answer

$$(-2, -9)$$

Question 5

A penny is thrown upward from a building. Its height in feet after $$t$$ seconds is given by $$h(t) = -16t^2$ + 24t + 75. $$When does it reach its maximum height?

Accepted Answer

$$t = 0.75$$\ sec$

Question 6

Given the polynomial $$f(x) = 4x^5$ + 3x^4$ - 7x + 9$$, what is the degree and what is the end behavior as $$x 	o -\infty$$?

Accepted Answer

Degree 5, left falls

Question 7

Which of the following is the correct set of possible rational zeros for $$f(x) = 7x^6$ - 2x^2$ + 9x - 12$$?

Accepted Answer

$$\pm1, \pm2, \pm3, \pm4, \pm6, \pm12, \pm\frac{1}{7}$$

Question 8

Find all zeros of $$f(x) = 2x^3$ + 33x^2$ - 90x$$ given that $$x = -5 is a $$zero.

Accepted Answer

$$-3, 6, -5$$

Question 9

Which graph best represents the function $$f(x) = \dfrac{1}{x-2}$$?

Accepted Answer

Image 6

Question 10

For the rational function $$f(x) = \dfrac{x^2$ + 3x - 4}{x^2$ - 2x}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 0, x = 2$$

Question 11

Solve the inequality $$x^3$$ + $$2x^2 - 4x - 45$$ \leq 0$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -9] \cup [0, 5]$$

Question 12

Given the graph in Image 1, which of the following is the vertex of the parabola?

Accepted Answer

$$(-2, -9)$$

Question 13

Given the function $$f(x) = 3x^3$ + 16x^2$ + 11x + 2$$, how many complex zeros does $$f(x)$$ have?

Accepted Answer

3

Question 14

Which of the following best describes the end behavior of $$f(x) = -4x^3$ - 4x^2$ + x + 4 as$$ $$x 	o \infty$$?

Accepted Answer

Falls to $$-\infty$$

Question 15

Divide $$4x^4$$ + $$2x^3$$ + $$10x^2 - x - 2$ by x^2$ + 2$$ and select the correct quotient.

Accepted Answer

$$4x^2 + 2x + 7$$ + \dfrac{16x + 22}{$$x^2 + 2$$}$$

Question 16

Which image best represents the graph of $$f(x) = \dfrac{x^2$ - 3}{x^2$ - 4}$$?

Accepted Answer

Image 7

Question 17

An athlete throws a shot put. Its height in feet is modeled by $$f(x) = -0.02x^2$ + 1.2x + 6.1$$, where $$x is $$the horizontal distance in feet. What is the maximum height?

Accepted Answer

$$24.1 ft$$

Question 18

For the rational function $$f(x) = \dfrac{2x^2$ + 3x - 6}{x^2$ - 2x}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 19

Solve the equation $$2x^2 + 3x + 6 = 0$ and select the correct solution.

Accepted Answer

$$x = \dfrac{-3 \pm i\sqrt{15}}{4}$$

Comprehensive College Algebra Study Guide: Quadratics, Polynomials, Rational Functions, and More

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