## Key Concepts

- Rational exponents can be rewritten several ways depending on what is most convenient for the problem. To solve a radical equation, both sides of the equation are raised to a power that will render the exponent on the variable equal to 1.
- Factoring extends to higher-order polynomials when it involves factoring out the GCF or factoring by grouping.
- We can solve radical equations by isolating the radical and raising both sides of the equation to a power that matches the index.
- To solve absolute value equations, we need to write two equations, one for the positive value and one for the negative value.
- Equations in quadratic form are easy to spot, as the exponent on the first term is double the exponent on the second term and the third term is a constant. We may also see a binomial in place of the single variable. We use substitution to solve.
- Solving a rational equation may also lead to a quadratic equation or an equation in quadratic form.

## Glossary

**absolute value equation**- an equation in which the variable appears in absolute value bars, typically with two solutions, one accounting for the positive expression and one for the negative expression

**equations in quadratic form**- equations with a power other than 2 but with a middle term with an exponent that is one-half the exponent of the leading term

**extraneous solutions**- any solutions obtained that are not valid in the original equation

**polynomial equation**- an equation containing a string of terms including numerical coefficients and variables raised to whole-number exponents

**radical equation**- an equation containing at least one radical term where the variable is part of the radicand