Chapter 1

If the terms of a polynomial do not have a GCF, does that mean it is not factorable? Explain.

How can you use factoring to simplify rational expressions?

Evaluate the following statement: The degree of a polynomial in standard form is the exponent of the leading term. Explain why the statement is true or false.

What does it mean when a radical does not have an index? Is the expression equal to the radicand? Explain.

Is \(2^{3}\) the same as \(3^{2} ?\) Explain.

Is \(\sqrt{2}\) an example of a rational terminating, rational repeating, or irrational number? Tell why it fits that category.

A polynomial is factorable, but it is not a perfect square trinomial or a difference of two squares. Can you factor the polynomial without fi ding the GCF?

Many times, multiplying two binomials with two variables results in a trinomial. Th s is not the case when there is a difference of two squares. Explain why the product in this case is also a binomial.

What is the order of operations? What acronym is used to describe the order of operations, and what does it stand for?

Tell whether the following statement is true or false and explain why: You only need to find the LCD when adding or subtracting rational expressions.

You can multiply polynomials with any number of terms and any number of variables using four basic steps over and over until you reach the expanded polynomial. What are the four steps?

Every number will have two square roots. What is the principal square root?

What is the purpose of scientific notation?

What do the Associative Properties allow us to do when following the order of operations? Explain your answer.

What is the purpose of scientific otation?

For the following exercises, find the greatest common factor. $$ 14 x+4 x y-18 x y^{2} $$

For the following exercises, simplify the rational expressions. $$ \frac{x^{2}-16}{x^{2}-5 x+4} $$

Simplify the rational expressions. $$ \frac{x^{2}-16}{x^{2}-5 x+4} $$

State whether the following statement is true and explain why or why not: A trinomial is always a higher degree than a monomial.

Can a radical with a negative radicand have a real square root? Why or why not?

For the following exercises, simplify the given expression. $$ 10+2 \cdot(5-3) $$

Explain what a negative exponent does.

Simplify the given expression. $$ 10+2 \cdot(5-3) $$

For the following exercises, find the greatest common factor. $$ 49 m b^{2}-35 m^{2} b a+77 m a^{2} $$

For the following exercises, simplify the rational expressions. $$ \frac{y^{2}+10 y+25}{y^{2}+11 y+30} $$

Simplify the rational expressions. $$ \frac{y^{2}+10 y+25}{y^{2}+11 y+30} $$

For the following exercises, simplify each expression. $$ \sqrt{256} $$

For the following exercises, identify the degree of the polynomial. $$ 7 x-2 x^{2}+13 $$

Simplify each expression. $$\sqrt{256}$$

For the following exercises, simplify the given expression. Write answers with positive exponents. $$9^{2}$$

Simplify the given expression. $$ 6 \div 2-\left(81 \div 3^{2}\right) $$

For the following exercises, find the greatest common factor. $$ 30 x^{3} y-45 x^{2} y^{2}+135 x y^{3} $$

For the following exercises, simplify the rational expressions. $$ \frac{6 a^{2}-24 a+24}{6 a^{2}-24} $$

Simplify the rational expressions. $$ \frac{6 a^{2}-24 a+24}{6 a^{2}-24} $$

For the following exercises, simplify each expression. $$ \sqrt{\sqrt{256}} $$

For the following exercises, identify the degree of the polynomial. $$ 14 m^{3}+m^{2}-16 m+8 $$

Simplify each expression. $$\sqrt{\sqrt{256}}$$

For the following exercises, simplify the given expression. Write answers with positive exponents. $$ 15^{-2} $$

Simplify the given expression. $$ 18+(6-8)^{3} $$

For the following exercises, find the greatest common factor. $$ 200 p^{3} m^{3}-30 p^{2} m^{3}+40 m^{3} $$

For the following exercises, simplify the rational expressions. $$ \frac{9 b^{2}+18 b+9}{3 b+3} $$

Simplify the rational expressions. $$ \frac{9 b^{2}+18 b+9}{3 b+3} $$

For the following exercises, simplify each expression. $$ \sqrt{4(9+16)} $$

For the following exercises, identify the degree of the polynomial. $$ -625 a^{8}+16 b^{4} $$

Simplify each expression. $$\sqrt{4(9+16)}$$

For the following exercises, simplify the given expression. Write answers with positive exponents. $$3^{2} \cdot 3^{3}$$

Simplify the given expression. $$ -2 \cdot\left[16 \div(8-4)^{2}\right]^{2} $$

For the following exercises, find the greatest common factor. $$ 36 j^{4} k^{2}-18 j^{3} k^{3}+54 j^{2} k^{4} $$

For the following exercises, simplify the rational expressions. $$ \frac{m-12}{m^{2}-144} $$

Simplify the rational expressions. $$ \frac{m-12}{m^{2}-144} $$