Question 1

Divide the following expression and simplify your answer: 
$$
\frac{7x^7$}{6y^2$}
$$

Accepted Answer

$$\frac{7x^7$}{6y^2$}$$

Question 2

Simplify the following expression: 
$$
(-25x^3$ - 30x^2$ - 13x + 7) + (5x + 4)
$$

Accepted Answer

$$-25x^3$$ - $$30x^2 - 8x + 11$

Question 3

Simplify the following expression: 
$$
(12x^3$ + x^2$ - 84x - 7) + (6x^2$ - 42)
$$

Accepted Answer

$$12x^3$$ + $$7x^2 - 84x - 49$

Question 4

Use the Remainder Theorem to find $$P(-9)$$ for $$P(x) = x^2$ + 13x + 31.$$

Accepted Answer

$$31 - 117 + 81 = -5 ($$but recalculate: $$(-9)^2 + 13(-9) + 31 = 81 - 117 + 31 = -5$)

Question 5

Solve for $$x$$: 
$$
x^2$ = 9
$$

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 6

A recent advertisement claims that 2 out of every 7 doctors recommend a supplement to increase energy levels. If a local hospital employs 91 doctors, how many would you expect to recommend the supplement? (Round to the nearest whole number.)

Accepted Answer

$$26$$

Question 7

Which of the following is the correct application of the Remainder Theorem for $$P(x) = x^2$ + 13x + 31$$ when $$c = -9$$?

Accepted Answer

$$P(-9) = (-9)^2$ + 13(-9) + 31$$

Question 8

Which of the following is the correct solution to the equation $$x^2 + 9x + 20 = 0$?

Accepted Answer

$$x = -4 or$$ $$x = -5$$

Question 9

If $$x^4 = 81$, what are all possible real solutions for x$?

Accepted Answer

$$x = 3, -3, 3i, -3i$$

Question 10

A hospital is conducting a survey. If 2 out of every 7 doctors recommend a supplement, and there are 140 doctors, how many do NOT recommend the supplement?

Accepted Answer

$$100$$

Question 11

Which of the following is the correct factorization of $$x^2 + 9x + 20$?

Accepted Answer

$$(x + 4)(x + 5)$$

Question 12

If $$x^2 + 13x + 31 = 0$, which of the following is the correct quadratic formula setup to solve for x$?

Accepted Answer

$$x = \frac{-13 \pm \sqrt{13^2$ - 4 \cdot 1 \cdot 31}}{2}$$

Question 13

Which of the following best describes the solution set for $$x^2 = -9$?

Accepted Answer

$$x = 3i or$$ $$x = -3i$$

Question 14

A company wants to divide $$7x^7$$ dollars equally among $$6y^2$$ employees. Which expression represents the amount each employee receives?

Accepted Answer

$$\frac{7x^7$}{6y^2$}$$

Question 15

If $$P(x) = x^2$ + 13x + 31$$, what is the remainder when $$P(x) is $$divided by $$x + 9$$?

Accepted Answer

$$-5$$

Question 16

Which of the following is the correct result of adding $$(12x^3$$ + $$x^2 - 84x - 7$$)$$ and (6x^2$ - 42)$$?

Accepted Answer

$$12x^3$$ + $$7x^2 - 84x - 49$

Question 17

If $$x^2 = 9$, which of the following statements is true?

Accepted Answer

$$x$$ can be either $$3 or$$ $$-3$$

Question 18

A hospital employs 70 doctors. If 2 out of every 7 recommend a supplement, how many do not recommend it?

Accepted Answer

$$50$$

Question 19

Which of the following is the correct solution to $$x^2 + 13x + 31 = 0$ using the quadratic formula?

Accepted Answer

$$x = \frac{-13 \pm \sqrt{169 - 124}}{2} = \frac{-13 \pm \sqrt{45}}{2}$$

Intermediate Algebra: Polynomial Operations, Synthetic Division, Remainder Theorem, and Equations

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