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Practice Test B

Find the x-intercepts of the graph of $f (x) = x^{2} + 5 x + 3 .$ $f (x) = x^{2} + 5 x + 3 .$
1. $\frac{- 5 \pm i \sqrt{13}}{2}$ $\frac{- 5 \pm i \sqrt{13}}{2}$
2. $\frac{- 5 \pm \sqrt{13}}{2}$ $\frac{- 5 \pm \sqrt{13}}{2}$
3. $\frac{- 5 \pm i \sqrt{37}}{2}$ $\frac{- 5 \pm i \sqrt{37}}{2}$
4. $\frac{- 5 \pm \sqrt{37}}{2}$ $\frac{- 5 \pm \sqrt{37}}{2}$
Which is the graph of $f (x) = 4 - {(x - 2)}^{2}$ $f (x) = 4 - {(x - 2)}^{2}$ ?
Find the vertex of the parabola described by $y = 6 x^{2} + 12 x - 5 .$ $y = 6 x^{2} + 12 x - 5 .$
1. $(- 1, - 11)$ $(- 1, - 11)$
2. $(1, - 5)$ $(1, - 5)$
3. $(- 1, 13)$ $(- 1, 13)$
4. (1, 13)
Which of the following is not in the domain of the function $f (x) = \frac{x^{2}}{x^{2} + x - 6} ?$ $f (x) = \frac{x^{2}}{x^{2} + x - 6} ?$
1. $- 3$ $- 3$
2. 0
3. 2
1. I and II
2. I and III
3. II and III
4. I only
Find the quotient and remainder when $x^{3} - 8 x + 6$ $x^{3} - 8 x + 6$ is divided by $x + 3 .$ $x + 3 .$
1. $x^{2} - 8; 2$ $x^{2} - 8; 2$
2. $x^{2} - 8; 0$ $x^{2} - 8; 0$
3. $x^{2} - 3 x + 1; x + 3$ $x^{2} - 3 x + 1; x + 3$
4. $x^{2} - 3 x + 1; 3$ $x^{2} - 3 x + 1; 3$
Which is the graph of the polynomial $P (x) = x^{4} + 2 x^{3}$ $P (x) = x^{4} + 2 x^{3}$ ?
Find all of the zeros of $f (x) = 3 x^{3} - 26 x^{2} + 61 x - 30$ $f (x) = 3 x^{3} - 26 x^{2} + 61 x - 30$ given that 3 is one of the zeros (that is, $f (3) = 0$ $f (3) = 0$ ).
1. $3, - 5, - \frac{2}{3}$ $3, - 5, - \frac{2}{3}$
2. $3, 2, \frac{5}{3}$ $3, 2, \frac{5}{3}$
3. $3, 5, \frac{2}{3}$ $3, 5, \frac{2}{3}$
4. $3, - 2, \frac{5}{3}$ $3, - 2, \frac{5}{3}$
Find the quotient that results from: $\frac{- 10 x^{3} + 21 x^{2} - 17 x + 12}{2 x - 3} .$ $\frac{- 10 x^{3} + 21 x^{2} - 17 x + 12}{2 x - 3} .$
1. $x^{2} - 3 x + 4$ $x^{2} - 3 x + 4$
2. $- 5 x^{2} + 3 x - 4$ $- 5 x^{2} + 3 x - 4$
3. $x^{2} + 3 x - 4$ $x^{2} + 3 x - 4$
4. $- 5 x^{2} - 4$ $- 5 x^{2} - 4$
Use the Remainder Theorem to find the value $P (- 3)$ $P (- 3)$ of the polynomial $P (x) = x^{4} + 4 x^{3} + 7 x^{2} + 10 x + 15 .$ $P (x) = x^{4} + 4 x^{3} + 7 x^{2} + 10 x + 15 .$
1. 13
2. 15
3. 21
4. 6
Find all distinct rational roots of the equation $- x^{3} + x^{2} + 8 x - 12 = 0$ $- x^{3} + x^{2} + 8 x - 12 = 0$ and then find the irrational roots if there are any.
1. $- 3$ $- 3$ and 2
2. $- 3$ $- 3$ and $\sqrt{2}$ $\sqrt{2}$
3. $- 1, - 2,$ $- 1, - 2,$ and 3
4. $- 3$ $- 3$ and $\sqrt{3}$ $\sqrt{3}$
Find the zeros of the polynomial function $f (x) = x^{3} + x^{2} - 30 x .$ $f (x) = x^{3} + x^{2} - 30 x .$
1. $x = - 6, x = 5, x = 0$ $x = - 6, x = 5, x = 0$
2. $x = 0, x = - 6$ $x = 0, x = - 6$
3. $x = 4, x = 5$ $x = 4, x = 5$
4. $x = 0, x = 4, x = 5$ $x = 0, x = 4, x = 5$
For $P (x) = x^{30} - 4 x^{25} + 6 x^{2} + 60,$ $P (x) = x^{30} - 4 x^{25} + 6 x^{2} + 60,$ list all possible rational zeros found by the Rational Zeros Test, but do not check to see which values are actually zeros.
1. $\pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 8, \pm 10, \pm 12, \pm 15, \pm 20, \pm 30,$ $\pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 8, \pm 10, \pm 12, \pm 15, \pm 20, \pm 30,$ and $\pm 60$ $\pm 60$
2. $\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 10, \pm 12, \pm 15, \pm 18, \pm 20, \pm 24, \pm 30,$ $\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 10, \pm 12, \pm 15, \pm 18, \pm 20, \pm 24, \pm 30,$ and $\pm 60$ $\pm 60$
3. $\pm 1, \pm 3, \pm 4, \pm 5, \pm 6, \pm 12, \pm 15, \pm 20, \pm 30,$ $\pm 1, \pm 3, \pm 4, \pm 5, \pm 6, \pm 12, \pm 15, \pm 20, \pm 30,$ and $\pm 60$ $\pm 60$
4. $\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 10, \pm 12, \pm 15, \pm 20, \pm 30,$ $\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 10, \pm 12, \pm 15, \pm 20, \pm 30,$ and $\pm 60$ $\pm 60$
Which of the following correctly describes the end behavior of $y = f (x) = {(x + 1)}^{2} {(x - 2)}^{2} ?$ $y = f (x) = {(x + 1)}^{2} {(x - 2)}^{2} ?$
1. ${\begin{cases} y \to \infty as x \to - \infty \\ y \to - \infty as x \to \infty \end{cases}$ ${\begin{cases} y \to \infty as x \to - \infty \\ y \to - \infty as x \to \infty \end{cases}$
2. ${\begin{cases} y \to - \infty as x \to - \infty \\ y \to - \infty as x \to \infty \end{cases}$ ${\begin{cases} y \to - \infty as x \to - \infty \\ y \to - \infty as x \to \infty \end{cases}$
3. ${\begin{cases} y \to \infty as x \to - \infty \\ y \to \infty as x \to \infty \end{cases}$ ${\begin{cases} y \to \infty as x \to - \infty \\ y \to \infty as x \to \infty \end{cases}$
4. ${\begin{cases} y \to - \infty as x \to - \infty \\ y \to \infty as x \to \infty \end{cases}$ ${\begin{cases} y \to - \infty as x \to - \infty \\ y \to \infty as x \to \infty \end{cases}$
Find the zeros and the multiplicity of each zero for $f (x) = (x^{2} - 1) {(x + 1)}^{2} .$ $f (x) = (x^{2} - 1) {(x + 1)}^{2} .$
1. ${\begin{array}{l} zero 1, & multiplicity 1 \\ zero - 1, & multiplicity 2 \end{array}$ ${\begin{array}{l} zero 1, & multiplicity 1 \\ zero - 1, & multiplicity 2 \end{array}$
2. ${\begin{array}{l} zero 1, & multiplicity 1 \\ zero - 1, & multiplicity 3 \end{array}$ ${\begin{array}{l} zero 1, & multiplicity 1 \\ zero - 1, & multiplicity 3 \end{array}$
3. ${\begin{array}{l} zero 1, & multiplicity 2 \\ zero - 1, & multiplicity 2 \end{array}$ ${\begin{array}{l} zero 1, & multiplicity 2 \\ zero - 1, & multiplicity 2 \end{array}$
4. ${\begin{array}{l} zero i, & multiplicity 2 \\ zero - 1, & multiplicity 2 \end{array}$ ${\begin{array}{l} zero i, & multiplicity 2 \\ zero - 1, & multiplicity 2 \end{array}$
Determine how many positive and how many negative real zeros the polynomial $P (x) = x^{5} - 4 x^{3} - x^{2} + 6 x - 3$ $P (x) = x^{5} - 4 x^{3} - x^{2} + 6 x - 3$ can have.
1. positive 3, negative 2
2. positive 2 or 0, negative 2 or 0
3. positive 3 or 1, negative 2 or 0
4. positive 2 or 0, negative 3 or 1
The horizontal and the vertical asymptotes of the graph of $f (x) = \frac{x^{2} + x - 2}{x^{2} + x - 12}$ $f (x) = \frac{x^{2} + x - 2}{x^{2} + x - 12}$ are
1. $x = - 2, y = 3, y = - 4 .$ $x = - 2, y = 3, y = - 4 .$
2. $x = 1, y = 3, y = - 4 .$ $x = 1, y = 3, y = - 4 .$
3. $y = 1, x = 3, x = - 4 .$ $y = 1, x = 3, x = - 4 .$
4. $y = - 2, x = 3, x = - 4 .$ $y = - 2, x = 3, x = - 4 .$
Write an equation that expresses the statement that S is directly proportional to the square of t and inversely proportional to the cube of x.
1. $S = \frac{k t^{3}}{\sqrt{3 x}}$ $S = \frac{k t^{3}}{\sqrt{3 x}}$
2. $S = k t^{2} x^{3}$ $S = k t^{2} x^{3}$
3. $S = \frac{k t^{3}}{x^{2}}$ $S = \frac{k t^{3}}{x^{2}}$
4. $S = \frac{k t^{2}}{x^{3}}$ $S = \frac{k t^{2}}{x^{3}}$
In Problem 17, suppose $S = 27$ $S = 27$ if $t = 3$ $t = 3$ and $x = 1 .$ $x = 1 .$ If $t = 6$ $t = 6$ and $x = 3,$ $x = 3,$ then what is S?
1. 54
2. 4
3. $\frac{4}{3}$ $\frac{4}{3}$
4. 9
The cost C of producing x thousand units of a product is given by

$C = x^{2} - 24 x + 319 (dollars) .$ $C = x^{2} - 24 x + 319 (dollars) .$

Find the value of x for which the cost is minimum.
1. 319
2. 12
3. 175
4. 24
From a rectangular $10 \times 12$ $10 \times 12$ piece of cardboard, four congruent squares with sides of length x are cut out, one at each corner. The sides can then be folded to form a box. Find the volume V of the box as a function of x.
1. $V = 2 x (10 - x) (12 - x)$ $V = 2 x (10 - x) (12 - x)$
2. $V = 2 x (10 - 2 x) (12 - 2 x)$ $V = 2 x (10 - 2 x) (12 - 2 x)$
3. $V = x (10 - x) (12 - x)$ $V = x (10 - x) (12 - x)$
4. $V = x (10 - 2 x) (12 - 2 x)$ $V = x (10 - 2 x) (12 - 2 x)$

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Table of Contents for Practice Test B

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Table of Contents for
Practice Test B