# Algebra 1 : Factoring Polynomials

## Example Questions

### Example Question #1 : Quadratic Equations

Simplify:

Explanation:

Change division into multiplication by the reciprocal which gives us the following

Now

this results in the following:

Simplification gives us

which equals

### Example Question #11 : Factoring Polynomials

Simplify .

Explanation:

Here, we simply need to identify that the numerator, , is a factor of the denominator. Let's start by factoring . The reverse FOIL method shows us that  multiplies to give us , so we can rewrite the fraction as . Canceling the common term gives us our answer of .

### Example Question #12 : Factoring Polynomials

Factor the polynomial completely

The polynomial cannot be factored further.

Explanation:

The coefficients 16 and 64 have greatest common factor 16; there is no variable that is shared by both terms. Therefore, we can distribute out 16:

cannot be factored further, so  is as far as we can go.

Explanation:

Explanation:

Explanation:

### Example Question #16 : Factoring Polynomials

Factor completely:

Explanation:

First, take out the greatest common factor of the terms. The GCF of 5 and 50 is 5 and the GCF of  and  is , so the GCF of the terms is .

When  is distributed out, this leaves .

is linear and thus prime, so no further factoring can be done.

### Example Question #11 : Factoring Polynomials

Factor the following polynomial.

Explanation:

This polynomial is a difference of two squares. The below formula can be used for factoring the difference of any two squares.

Using our given equation as , we can find the values to use in our factoring.

### Example Question #12 : Factoring Polynomials

Factor

Explanation:

When factoring a polynomial that has no coefficient in front of the  term, you begin by looking at the last term of the polynomial, which is .  You then think of all the factors of  that when added together equal , the coefficient in front of the  term.  The only combination of factors of  that can satisfy this condition is  and .  Thus, the factors of the polynomial are .