Question 1

Which of the following is the correct factorization of the polynomial $$x^3$$ - $$6x^2 + 11x - 6$?

Accepted Answer

$$ (x - 1)(x - 2)(x - 3) $$

Question 2

Solve the equation $$2x + 5 = 17$$ for $$x.$$

Accepted Answer

$$ x = 6 $$

Question 3

Which of the following is a solution to the quadratic equation $$x^2 - 4x + 3 = 0$?

Accepted Answer

$$ x = 1 $$

Question 4

Simplify the rational expression $$\frac{x^2$ - 9}{x^2$ - 6x + 9}.$$

Accepted Answer

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

Question 5

Which of the following is equivalent to $$\sqrt{50}$$?

Accepted Answer

$$ 5\sqrt{2} $$

Question 6

Solve for $$x$$: $$|2x - 5| = 9.$$

Accepted Answer

$$ x = 7  or$$ $$x = -2 $$

Question 7

Which of the following is the sum of the complex numbers $$3 + 4i$$ and $$2 - 7i$$?

Accepted Answer

$$ 5 - 3i $$

Question 8

A chemist needs to mix a $$20\%$$ saline solution with a $$50\%$$ saline solution to obtain $$10$$ liters of a $$30\%$$ solution. How many liters of the $$20\%$$ solution should be used?

Accepted Answer

$$ 6.67 $$ liters

Question 9

Which of the following is the correct solution to the inequality $$2x - 3 \u003e 7$$?

Accepted Answer

$$ x \u003e 5 $$

Question 10

If $$f(x) = x^2$ - 4x + 7$$, what is $$f(3)$$?

Accepted Answer

$$ 4 $$

Question 11

Which of the following is the conjugate of the complex number $$5 - 2i$$?

Accepted Answer

$$ 5 + 2i $$

Question 12

Solve the radical equation: $$\sqrt{x + 3} = 5.$$

Accepted Answer

$$ x = 22 $$

Question 13

Which of the following is the correct simplification of $$\frac{2x^2$ - 8}{4x}$$?

Accepted Answer

$$ \frac{x - 2}{2x} $$

Question 14

A bank offers an annual interest rate of $$5\%$$ compounded annually. If you invest $$\1000$, how much will you have after 2$ years?

Accepted Answer

$$ 1102.50 $$

Question 15

Which of the following is the solution set for $$|x + 2| \leq 5$$?

Accepted Answer

$$ -7 \leq x \leq 3 $$

College Algebra: Foundations, Equations, and Inequalities

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