# Precalculus Examples

Step 1

Set equal to .

Step 2

Step 2.1

Factor the left side of the equation.

Step 2.1.1

Factor out of .

Step 2.1.1.1

Factor out of .

Step 2.1.1.2

Factor out of .

Step 2.1.1.3

Factor out of .

Step 2.1.1.4

Factor out of .

Step 2.1.1.5

Factor out of .

Step 2.1.2

Factor.

Step 2.1.2.1

Factor by grouping.

Step 2.1.2.1.1

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

Step 2.1.2.1.1.1

Factor out of .

Step 2.1.2.1.1.2

Rewrite as plus

Step 2.1.2.1.1.3

Apply the distributive property.

Step 2.1.2.1.2

Factor out the greatest common factor from each group.

Step 2.1.2.1.2.1

Group the first two terms and the last two terms.

Step 2.1.2.1.2.2

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

Step 2.1.2.1.3

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

Step 2.1.2.2

Remove unnecessary parentheses.

Step 2.2

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Step 2.3

Set equal to .

Step 2.4

Set equal to and solve for .

Step 2.4.1

Set equal to .

Step 2.4.2

Solve for .

Step 2.4.2.1

Add to both sides of the equation.

Step 2.4.2.2

Divide each term in by and simplify.

Step 2.4.2.2.1

Divide each term in by .

Step 2.4.2.2.2

Simplify the left side.

Step 2.4.2.2.2.1

Cancel the common factor of .

Step 2.4.2.2.2.1.1

Cancel the common factor.

Step 2.4.2.2.2.1.2

Divide by .

Step 2.5

Set equal to and solve for .

Step 2.5.1

Set equal to .

Step 2.5.2

Add to both sides of the equation.

Step 2.6

The final solution is all the values that make true.

Step 3