Insert the required factor in parentheses.

$$\frac{7 x^2}{10}=\frac{7}{10}(\quad)$$

Completely factor the difference of two squares.

$$x^2-49$$

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. xy<0

Match the polynomial with its description. [The polynomials are labeled (a), (b), (c), (d), (e), and (f).] (a) $3 x^2$ (b) $1-2 x^3$ (c) $x^3+3 x^2+3 x+1$ (d) 12 (e) $-3 x^5+2 x^3+x$ (f) $\frac{2}{3} x^4+x^2+10$

A trinomial of degree 5

Find the domain of the expression.

$$2 x^2+5 x-2$$

Describe and correct the error.

$$5 z+3(x-2)=5 z+3 x-2$$

Write the expression as a repeated multiplication problem.

$$(-2)^7$$

Find the distance between the real numbers $-5.4$ and $3 \frac{3}{4}$.

Find an example for which

$$|a-b|>|a|-|b| \text {, }$$

and an example for which

$$|a-b|=|a|-|b| \text {. }$$

Then prove that

$$\begin{aligned} &|a-b| \geq|a|-|b| \\ &\text { for all } a, b \text {. } \end{aligned}$$

Find the greatest common factor of the expressions.

$$36,84,294$$

Determine which numbers in the set are irrational numbers.

$$-9,-\frac{7}{2}, 5, \frac{2}{3}, \sqrt{2}, 0,1,-4,2,-11$$

Determine which numbers in the set are irrational numbers.

$$\left\{11,-14,-\frac{8}{9}, \frac{5}{2}, \sqrt{6}, 0.4\right\}$$

Determine which numbers in the set are rational numbers.

$$-9,-\frac{7}{2}, 5, \frac{2}{3}, \sqrt{2}, 0,1,-4,2,-11$$

Determine which numbers in the set are rational numbers

$$\left\{11,-14,-\frac{8}{9}, \frac{5}{2}, \sqrt{6}, 0.4\right\}$$