# Precalculus Examples

,

Roots are the points where the graph intercepts with the x-axis .

at the roots

The root at was found by solving for when and .

The factor is

The root at was found by solving for when and .

The factor is

Combine all the factors into a single equation.

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Move to the left of .

Combine and .

Multiply .

Multiply by .

Combine and .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of .

Multiply by .

Subtract from .

Factor by grouping.

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

Factor out of .

Rewrite as plus

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by by adding the exponents.

Move .

Multiply by .

Multiply by .

Rewrite as .

Multiply by .

Subtract from .

Split the fraction into two fractions.

Split the fraction into two fractions.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.