# Algebra Examples

To find the roots/zeros of the function, set the function equal to and solve.

Regroup terms.

Rewrite as .

Since both terms are perfect cubes, factor using the sum of cubes formula, where and .

Simplify.

Multiply by .

Raise to the power of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Add and .

Factor using the perfect square rule.

Rewrite as .

Check the middle term by multiplying and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule , where and .

Set the factor equal to .

Subtract from both sides of the equation.

Solve the equations for . The multiplicity of a root is the number of times the root appears. For example, a factor of would have a root at with multiplicity of .

(Multiplicity of )