Question 1

Factor the expression $$27a^4$$ - $$12b^2$$ completely.

Accepted Answer

$$3(3a^2$$ - $$2b)(3a^2 + 2b$$)$$

Question 2

Given the piecewise function $$f(x) = \begin{cases} 9x + 1, & x  12 \end{cases}$$, what is the value of $$2f(-7) + 3f(10)$$?

Accepted Answer

$$2(-62) + 3(70) = 86$$

Question 3

Express $$\sqrt{-112} in $$terms of $$i.$$

Accepted Answer

$$4\sqrt{7}i$$

Question 4

Simplify $$(-8 + 16i) - (6 - 3i)$$ and write your answer in the form $$a + bi.$$

Accepted Answer

$$-14 + 19i$$

Question 5

If $$x^2 + 8x + 16 = 10$, what are the solutions for x$?

Accepted Answer

$$x = -4 \pm \sqrt{10}$$

Question 6

A real estate investment's yearly income is modeled by $$I(t) = -0.1t^2$ + 1.6t. $$After what year does the income begin to decline?

Accepted Answer

$$t = 8$$

Question 7

A projectile is thrown upward so that its height after $$t$$ seconds is $$h(t) = -16t^2$ + 312t. $$After how many seconds does it reach its maximum height?

Accepted Answer

$$t = 9.75$$

Question 8

Find the zeros and their multiplicities for $$f(x) = -5x^2$(x - 6)(x + 1)^3$.

Accepted Answer

Zeros: $$x = 0 ($$multiplicity 2), $$x = 6 ($$multiplicity 1), $$x = -1 ($$multiplicity 3)

Question 9

A soccer league has 10 teams, each playing every other team twice. If the cost per game is $$44, what is the total cost for the season? (Use N(x$$) = $$x^2 - x$ for the number of games.)

Accepted Answer

$$3960$$

Question 10

Use long division to divide $$P(x) = 2x^3$ + 4x^2$ - 6x + 2 by$$ $$d(x) = 2x + 2. $$What is the quotient $$Q(x)$$ and remainder $$R(x)$$?

Accepted Answer

$$Q(x) = x^2$ + x - 4$$, $$R(x) = 10$$

Question 11

Find a cubic polynomial with real coefficients whose zeros are $$-2$$, $$2$$, and $$5.$$

Accepted Answer

$$f(x) = (x + 2)(x - 2)(x - 5)$$

Question 12

Suppose a degree 6 polynomial with rational coefficients has zeros $$2i$$, $$-4 + 4i$$, and $$4 - \sqrt{5}. $$Which of the following lists all the other zeros?

Accepted Answer

$$-2i$$, $$-4 - 4i$$, $$4 + \sqrt{5}$$

Question 13

Given $$f(x) = x^3$ + 4x^2$ - 2x - 8$$, which of the following is a rational zero?

Accepted Answer

$$x = 2$$

Question 14

Which of the following lists all possible rational zeros for $$f(x) = -2x^4$ + 5x^3$ + 4x^2$ + 18$$ according to the Rational Root Theorem?

Accepted Answer

$$\pm1, \pm2, \pm3, \pm6, \pm9, \pm18, \pm\frac{1}{2}, \pm\frac{3}{2}, \pm\frac{9}{2}$$

Question 15

If $$M(x) = 4x - x^2$ models the number of mosquitoes (in millions) as a function of June rainfall x$ (in inches), what rainfall produces the maximum number of mosquitoes?

Accepted Answer

$$x = 2$$

Question 16

Find the vertex of the parabola $$f(x) = -4x^2$ - 16x - 21.$$

Accepted Answer

Question 17

Given $$f(x) = x^2$ - 2x - 8$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = -2, 4$$

Question 18

Which of the following is the correct factorization of $$x^3$$ - $$10x^2 + 27x - 18$?

Accepted Answer

$$(x - 1)(x - 3)(x - 6)$$

Question 19

If $$g(x) = -x(x + 3)(x - 2)^2$, what is the degree and leading coefficient of g(x$$)$$?

Accepted Answer

Degree: 4, Leading coefficient: $$-1$$

College Algebra Test #2 Review – Step-by-Step Study Guidance

Study Guide - Practice Questions

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