# High School Math : Factoring Polynomials

## Example Questions

### Example Question #1 : Factoring Polynomials

Factor

Cannot be Factored

Explanation:

Use the difference of perfect cubes equation:

In ,

and

### Example Question #2 : Factoring Polynomials

Factor the polynomial completely and solve for .

Explanation:

To factor and solve for  in the equation

Factor  out of the equation

Use the "difference of squares" technique to factor the parenthetical term, which provides the completely factored equation:

Any value that causes any one of the three terms , and  to be  will be a solution to the equation, therefore

### Example Question #1 : Factoring Polynomials

Factor the following expression:

Explanation:

You can see that each term in the equation has an "x", therefore by factoring "x" from each term you can get that the equation equals .

### Example Question #4 : Factoring Polynomials

Factor this expression:

Explanation:

First consider all the factors of 12:

1 and 12

2 and 6

3 and 4

Then consider which of these pairs adds up to 7.  This pair is 3 and 4.

### Example Question #1 : Factoring Polynomials

Find the zeros.

Explanation:

This is a difference of perfect cubes so it factors to . Only the first expression will yield an answer when set equal to 0, which is 1. The second expression will never cross the -axis. Therefore, your answer is only 1.

### Example Question #2 : Factoring Polynomials

Find the zeros.

Explanation:

Factor the equation to . Set  and get one of your 's to be . Then factor the second expression to . Set them equal to zero and you get

### Example Question #21 : Polynomials

Factor the following polynomial:

Explanation:

Begin by extracting  from the polynomial:

Now, factor the remainder of the polynomial as a difference of cubes:

### Example Question #6 : Factoring Polynomials

Factor the following polynomial:

Explanation:

Begin by rearranging like terms:

Now, factor out like terms:

Rearrange the polynomial:

### Example Question #7 : Factoring Polynomials

Factor the following polynomial:

Explanation:

Begin by rearranging like terms:

Now, factor out like terms:

Rearrange the polynomial:

Factor:

### Example Question #8 : Factoring Polynomials

Factor the following polynomial: