2.8 Review Exercise
Chapter
Chapter 2
Section
2.8
11mathHarcourt2.8 92 Videos

Simplify each of the following: \displaystyle \left(4 x^{3}-5 x+6\right)-\left(2 x^{2}-x+3\right)

Q1a

Simplify each of the following: \displaystyle \left(4 x^{2}\right)(5 x)\left(6 x^{3}\right)

Q1b

Simplify each of the following: \displaystyle 4\left(2 x^{2}\right)^{3}

Q1c

Simplify each of the following: \displaystyle (3 x)^{2}-3 x^{2}

Q1d

Simplify each of the following: \displaystyle 2 x^{2}\left(3 x^{2}-2 x+1\right)

Q1e

Simplify each of the following: \displaystyle 25 x^{4} \div 5 x

Q1f

Simplify each of the following: \displaystyle 3 x(4 x-5 x-6 x)

Q1g

Simplify each of the following: \displaystyle \left(3 x^{2}-4 x^{2}\right)^{2}

Q1h

Simplify each of the following: \displaystyle \left(7 x^{2}-8 x^{2}\right)(7 x-8 x)

Q1i

Simplify each of the following: \displaystyle 3\left(x^{2}-2 x+1\right)-x(1-x)

Q2a

Simplify each of the following: \displaystyle (2 x-1)\left(x^{2}+x+2\right)

Q2b

Simplify each of the following: \displaystyle 3 x(2 x-1)(x+2)

Q2c

Simplify each of the following: \displaystyle 4(3 x-2)^{2}

Q2d

Simplify each of the following: \displaystyle (3 x+1)^{3}

Q2e

Simplify each of the following: \displaystyle (x-2)(x+3)-(x+2)(x-3)

Q2f

Simplify each of the following: \displaystyle (2 x+1)^{2}-(x+2)^{2}

Q2g

Simplify each of the following: \displaystyle 1-x(1-x)^{2}

Q2h

If \displaystyle f(x)=2 x+1  and \displaystyle g(x)=x+2 , find expressions for the following:

\displaystyle 3 f(x)-2 g(x)

Q3a

If \displaystyle f(x)=2 x+1  and \displaystyle g(x)=x+2 , find expressions for the following:

\displaystyle 6 f(x) g(x)

Q3b

If \displaystyle f(x)=2 x+1  and \displaystyle g(x)=x+2 , find expressions for the following:

\displaystyle [f(x)]^{2}+[g(x)]^{2}

Q3c

If \displaystyle f(x)=2 x+1  and \displaystyle g(x)=x+2 , find expressions for the following:

\displaystyle [f(x)-g(x)]^{2}

Q3d

If \displaystyle f(x)=2 x^{2}-3 x+1 , find the simplified expression for \displaystyle g(x)  in each of the following:

\displaystyle g(x)=f(x+1)

Q4a

If \displaystyle f(x)=2 x^{2}-3 x+1 , find the simplified expression for \displaystyle g(x)  in each of the following:

\displaystyle g(x)=f(2 x)

Q4b

If \displaystyle f(x)=2 x^{2}-3 x+1 , find the simplified expression for \displaystyle g(x)  in each of the following:

\displaystyle g(x)=f(-x)

Q4c

If \displaystyle f(x)=2 x^{2}-3 x+1 , find the simplified expression for \displaystyle g(x)  in each of the following:

\displaystyle g(x)=2 f(x-1)-12

Q4d

Find the simplified expression for the perimeter and area of the given figure.

Q5

Change the following to mixed radicals in simplest form.

\displaystyle \sqrt{128}

Q6a

Change the following to mixed radicals in simplest form.

\displaystyle 3 \sqrt{72}

Q6b

Change the following to mixed radicals in simplest form.

\displaystyle \sqrt{800}

Q6c

Change the following to mixed radicals in simplest form.

\displaystyle 5 \sqrt{32}

Q6d

Change the following to mixed radicals in simplest form.

\displaystyle 3 \sqrt{175}

Q6e

Simplify each of the following:

\displaystyle 3 \sqrt{5} \times 2 \sqrt{7}

Q7a

Simplify each of the following:

\displaystyle 4 \sqrt{3} \times 2 \sqrt{6}

Q7b

Simplify each of the following:

\displaystyle 3 \sqrt{5}-5 \sqrt{3}+\sqrt{5}-\sqrt{3}

Q7c

Simplify each of the following:

\displaystyle \sqrt{20}+\sqrt{40}+\sqrt{80}

Q7d

Simplify each of the following:

\displaystyle 3 \sqrt{12}+2 \sqrt{48}

Q7e

Simplify each of the following:

\displaystyle \sqrt{3}(2 \sqrt{3}-3 \sqrt{2})

Q7f

Simplify each of the following:

\displaystyle (3+\sqrt{2})^{2}

Q7g

Simplify each of the following:

\displaystyle (2 \sqrt{3}+3)(2 \sqrt{3}-3)

Q7h

Simplify each of the following:

\displaystyle (3 \sqrt{2}+4 \sqrt{5})(3 \sqrt{2}-4 \sqrt{5})

Q7i

Factor completely each of the following:

\displaystyle 9 x^{2}-18 x

Q8a

Factor completely each of the following:

\displaystyle x^{2}-18 x-19

Q8b

Factor completely each of the following:

\displaystyle 9 x^{2}-18 x+9

Q8c

Factor completely each of the following:

\displaystyle x^{4}+5 x^{2}+4

Q8d

Factor completely each of the following:

\displaystyle x^{4}-10 x^{2}+9

Q8e

Factor completely each of the following:

\displaystyle 4 x^{2}+15 x-4

Q8f

Factor completely each of the following:

\displaystyle (2 x+3)^{2}-9

Q8g

Factor completely each of the following:

\displaystyle (x+1)^{2}-3(x+1)

Q8h

Factor completely each of the following:

\displaystyle x^{2}(2 x-1)-4(2 x-1)

Q8i

Factor completely each of the following:

\displaystyle 6 x^{2}+7 x-10

Q8j

Factor completely each of the following: \displaystyle 4 x^{3}-12 x^{2}+9 x

Q8k

Factor completely each of the following: \displaystyle 5 x^{4}-10 x^{3}-3 x^{2}+6 x

Q8l

Solve each of the following for x and graph the solution on a number line. \displaystyle 1-2 x < 3

Q9a

Solve each of the following for x and graph the solution on a number line. \displaystyle 2 x-4 < x

Q9b

Solve each of the following for x and graph the solution on a number line. \displaystyle 3 x+5 \leq x-3

Q9c

Solve each of the following for x and graph the solution on a number line. \displaystyle 2 x-3 > 4 x-6

Q9d

Solve each of the following for x and graph the solution on a number line. \displaystyle 3(4-x) \geq 4(3-x)

Q9e

Solve each of the following for x and graph the solution on a number line. \displaystyle 1-2(3-x) > x-6

Q9f

Solve and graph each of the following on a number line. \displaystyle -3 \leq x+2 \leq 3

Q10a

Solve and graph each of the following on a number line. \displaystyle 2 x-1 < 3  or \displaystyle 2 x-1 > 7

Q10b

State any restrictions on the variable in each of the following: \displaystyle \frac{2 x+4}{6}

Q11a

State any restrictions on the variable in each of the following: \displaystyle \frac{4}{4 x-8}

Q11b

State any restrictions on the variable in each of the following: \displaystyle \frac{3}{2 x-1}

Q11c

State any restrictions on the variable in each of the following: \displaystyle \frac{2}{x^{2}-4}

Q11d

State any restrictions on the variable in each of the following: \displaystyle \frac{x}{x^{2}+x}

Q11e

State any restrictions on the variable in each of the following: \displaystyle \frac{1}{x^{2}-2 x+1}

Q11f

State any restrictions on the variable in each of the following: \displaystyle \frac{3 x}{x^{2}+3 x-4}

Q11g

State any restrictions on the variable in each of the following: \displaystyle \frac{1}{x^{3}-x^{2}-2 x}

Q11h

State any restrictions on the variable in each of the following: \displaystyle \frac{x-3}{x^{2}-8 x+15}

Q11i

Simplify each of the following: \displaystyle \frac{3}{6 x-9}

Q12a

Simplify each of the following: \displaystyle \frac{2 x}{x^{2}+x}

Q12b

Simplify each of the following: \displaystyle \frac{x+1}{x^{2}-1}

Q12c

Simplify each of the following: \displaystyle \frac{2 x+4}{3 x+6}

Q12d

Simplify each of the following: \displaystyle \frac{x^{2}-4}{2 x-4}

Q12e

Simplify each of the following: \displaystyle \frac{3 x^{2}-3}{x^{3}-x}

Q12f

Simplify each of the following: \displaystyle \frac{x^{2}+2 x-3}{x^{2}-2 x+1}

Q12g

Simplify each of the following: \displaystyle \frac{x^{2}-4}{x^{2}-4 x+4}

Q12h

Simplify each of the following: \displaystyle \frac{2 x^{2}+5 x-12}{2 x^{2}+11 x+12}

Q12i

Simplify each of the following: \displaystyle \frac{3 x}{4} \div \frac{6}{x}

Q13a

Simplify each of the following: \displaystyle \frac{x-2}{3} \times \frac{6}{5 x-10}

Q13b

Simplify each of the following: \displaystyle \frac{(x-2)^{2}}{x^{2}-4} \times \frac{x+2}{x}

Q13c

Simplify each of the following: \displaystyle \frac{3-x}{4 x} \div \frac{x^{2}-9}{8}

Q13d

Simplify each of the following: \displaystyle \frac{2 x-6}{3 x+6} \times \frac{x^{2}+5 x+6}{4 x^{2}-36}

Q13e

Simplify each of the following: \displaystyle \frac{x-x^{3}}{x^{2}-2 x-3} \div \frac{x^{2}-x}{2 x-6}

Q13f

Simplify each of the following; \displaystyle \frac{3}{x}+\frac{2}{x-1}

Q14a

Simplify each of the following; \displaystyle \frac{2}{x-1}-\frac{1}{x+2}

Q14b

Simplify each of the following; \displaystyle \frac{x+1}{x}-\frac{x}{x+1}

Q14c

Simplify each of the following; \displaystyle 3+\frac{3}{x-1}

Q14d

Simplify each of the following; \displaystyle \frac{4}{x-1}+\frac{5}{x^{2}-1}

Q14e

Simplify each of the following; \displaystyle \frac{x+1}{x^{2}-x}+\frac{x-1}{x^{2}+x}

Simplify each of the following: \displaystyle \frac{x^{2}-x}{x^{2}-x-2} \times \frac{x^{2}-1}{x^{2}-2 x} \div \frac{x^{2}-2 x+1}{x^{2}-4 x+4}
Simplify each of the following: \displaystyle \frac{x}{x^{2}-4}-\frac{x-2}{x^{2}+2 x}+\frac{x+2}{x^{2}-2 x}