Chapter 1

How can you use factoring to simplify rational expressions?

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

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.

Many times, multiplying two binomials with two variables results in a trinomial. This 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.

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.

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

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

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?

Explain what a negative exponent does.

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

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

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, identify the degree of the polynomial. \(7 x-2 x^{2}+13\)

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

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

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

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, identify the degree of the polynomial. \(14 m^{3}+m^{2}-16 m+8\)

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

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

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

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, identify the degree of the polynomial. \(-625 a^{8}+16 b^{4}\)

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

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

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

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, identify the degree of the polynomial. \(200 p-30 p^{2} m+40 m^{3}\)

For the following exercises, simplify each expression. \(\sqrt{289}-\sqrt{121}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(4^{4} \div 4\)

For the following exercises, simplify the rational expressions. \(\frac{2 x^{2}+7 x-4}{4 x^{2}+2 x-2}\)

For the following exercises, find the greatest common factor. \(6 y^{4}-2 y^{3}+3 y^{2}-y\)

For the following exercises, identify the degree of the polynomial. \(x^{2}+4 x+4\)

For the following exercises, simplify each expression. \(\sqrt{196}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(2^{2}\right)^{-2}\)

For the following exercises, simplify the rational expressions. \(\frac{6 x^{2}+5 x-4}{3 x^{2}+19 x+20}\)

For the following exercises, factor by grouping. \(6 x^{2}+5 x-4\)

For the following exercises, identify the degree of the polynomial. \(6 y^{4}-y^{5}+3 y-4\)

For the following exercises, simplify each expression. \(\sqrt{1}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \((5-8)^{0}\)

For the following exercises, simplify the rational expressions. \(\frac{a^{2}+9 a+18}{a^{2}+3 a-18}\)

For the following exercises, factor by grouping. \(2 a^{2}+9 a-18\)

For the following exercises, find the sum or difference. \(\left(12 x^{2}+3 x\right)-\left(8 x^{2}-19\right)\)