Evaluate each expression if $p=-4, q=8$, and $r=-10$. See the mentioned example.

$$\dfrac{-(p+2)^2-3 r}{2-q}$$

Justify each statement by giving the correct property of absolute value. Assume all variables represent real numbers. See the example in this section.

$$|12+11 r| \geq 0$$

Match each polynomial in Column I with its factored form in Column II.

$$\begin{array}{ll} \textbf{Column I} \qquad \quad & \textbf{Column II} \\ 27-8 x^3 \quad & \text{A. } (3-2 x)\left(9+6 x+4 x^2\right)\\ &\text{B. } (2 x-3)\left(4 x^2+6 x+9\right) \\ &\text{C. } (2 x+3)\left(4 x^2-6 x+9\right)\\ \end{array}$$

Match each polynomial in Column I with its factored form in Column II.

$$\begin{array}{ll} \textbf{Column I} \qquad \quad & \textbf{Column II} \\ 8 x^3+27 \quad & \text{A. } (3-2 x)\left(9+6 x+4 x^2\right)\\ &\text{B. } (2 x-3)\left(4 x^2+6 x+9\right) \\ &\text{C. } (2 x+3)\left(4 x^2-6 x+9\right)\\ \end{array}$$

Match each polynomial in Column I with its factored form in Column II.

$$\begin{array}{ll} \textbf{Column I} \qquad \quad & \textbf{Column II} \\ 8 x^3-27 \quad & \text{A. } (3-2 x)\left(9+6 x+4 x^2\right)\\ &\text{B. } (2 x-3)\left(4 x^2+6 x+9\right) \\ &\text{C. } (2 x+3)\left(4 x^2-6 x+9\right)\\ \end{array}$$

Evaluate each expression if $p=-4, q=8$, and $r=-10$. See the mentioned example.

$$\dfrac{\dfrac{q}{4}-\dfrac{r}{5}}{\dfrac{p}{2}+\dfrac{q}{2}}$$

Simplify each expression. See the example in this section.

$$(-64)^{1 / 4}$$

Justify each statement by giving the correct property of absolute value. Assume all variables represent real numbers. See the example in this section.

$$|5+x| \leq|5|+|x|$$

Simplify each expression. Assume all variables represent positive real numbers. See the examples in this section.

$$\sqrt{24 m^6 n^5}$$

Perform each addition or subtraction. See the example in this section.

$$\dfrac{3}{z}+\dfrac{x}{z^2}$$

Perform each division.

$$\dfrac{72 r^2+59 r+12}{8 r+3}$$

Find each product. See the examples in this section.

$$(r-3 s+t)(2 r-s+t)$$

Match each polynomial in Column I with its factored form in Column II.

$$\begin{array}{ll} \textbf{Column I} \qquad \quad & \textbf{Column II} \\ 25 y^2-x^2 \quad & \text{A. } (x+5 y)(x-5 y) \\ &\text{B. } (x+5 y)^2 \\ &\text{C. } (x-5 y)^2\\ &\text{D. } (5 y+x)(5 y-x)\\ \end{array}$$

Match each polynomial in Column I with its factored form in Column II.

$$\begin{array}{ll} \textbf{Column I} \qquad \quad & \textbf{Column II} \\ x^2-25 y^2 \quad & \text{A. } (x+5 y)(x-5 y) \\ &\text{B. } (x+5 y)^2 \\ &\text{C. } (x-5 y)^2\\ &\text{D. } (5 y+x)(5 y-x)\\ \end{array}$$