# Precalculus Examples

To find the x-intercept, substitute in for and solve for .

Rewrite the equation as .

Move to the right side of the equation by subtracting from both sides of the equation.

Move to the left side of the equation by subtracting it from both sides.

Factor the left side of the equation.

Rewrite as .

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

Simplify.

Multiply by .

One to any power is one.

Set equal to and solve for .

Set the factor equal to .

Add to both sides of the equation.

Set equal to and solve for .

Set the factor equal to .

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

One to any power is one.

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Multiply by .

Simplify the denominator.

Rewrite.

Multiply by .

Simplify the expression to solve for the portion of the .

Simplify the numerator.

One to any power is one.

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Multiply by .

Simplify the denominator.

Rewrite.

Multiply by .

-----Begin simplification-----

Rewrite as .

Factor out of .

Factor out of .

Move .

Multiply by .

Factor out of .

Move the negative in front of the fraction.

Simplify the expression to solve for the portion of the .

Simplify the numerator.

One to any power is one.

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Multiply by .

Simplify the denominator.

Rewrite.

Multiply by .

-----Begin simplification-----

Rewrite as .

Move .

Factor out of .

Move the negative in front of the fraction.

The final answer is the combination of both solutions.

The solution is the result of and .

To find the y-intercept, substitute in for and solve for .

Simplify each term.

Remove parentheses around .

Raising to any positive power yields .

Subtract from .

These are the and intercepts of the equation .

x-intercept:

y-intercept: