# Precalculus Examples

, ,

Step 1

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

at the roots

Step 2

The root at was found by solving for when and .

The factor is

Step 3

The root at was found by solving for when and .

The factor is

Step 4

The root at was found by solving for when and .

The factor is

Step 5

Combine all the factors into a single equation.

Step 6

Step 6.1

Expand using the FOIL Method.

Step 6.1.1

Apply the distributive property.

Step 6.1.2

Apply the distributive property.

Step 6.1.3

Apply the distributive property.

Step 6.2

Simplify and combine like terms.

Step 6.2.1

Simplify each term.

Step 6.2.1.1

Multiply by .

Step 6.2.1.2

Move to the left of .

Step 6.2.1.3

Rewrite as .

Step 6.2.1.4

Multiply by .

Step 6.2.2

Subtract from .

Step 6.3

Expand by multiplying each term in the first expression by each term in the second expression.

Step 6.4

Simplify terms.

Step 6.4.1

Simplify each term.

Step 6.4.1.1

Multiply by by adding the exponents.

Step 6.4.1.1.1

Multiply by .

Step 6.4.1.1.1.1

Raise to the power of .

Step 6.4.1.1.1.2

Use the power rule to combine exponents.

Step 6.4.1.1.2

Add and .

Step 6.4.1.2

Move to the left of .

Step 6.4.1.3

Multiply by by adding the exponents.

Step 6.4.1.3.1

Move .

Step 6.4.1.3.2

Multiply by .

Step 6.4.1.4

Multiply by .

Step 6.4.1.5

Multiply by .

Step 6.4.2

Simplify by adding terms.

Step 6.4.2.1

Subtract from .

Step 6.4.2.2

Add and .

Step 7