### All High School Math Resources

## Example Questions

### Example Question #1 : Factoring Polynomials

Factor

**Possible Answers:**

Cannot be Factored

**Correct answer:**

Use the difference of perfect cubes equation:

In ,

and

### Example Question #2 : Factoring Polynomials

Factor the polynomial **completely** and solve for *.*

**Possible Answers:**

**Correct answer:**

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 #3 : Factoring Polynomials

Factor the following expression:

**Possible Answers:**

**Correct answer:**

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 #2 : Factoring Polynomials

Factor this expression:

**Possible Answers:**

**Correct answer:**

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.

Therefore the answer is .

### Example Question #1 : Factoring Polynomials

Find the zeros.

**Possible Answers:**

**Correct answer:**

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 #3 : Factoring Polynomials

Find the zeros.

**Possible Answers:**

**Correct answer:**

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 #6 : Factoring Polynomials

Factor the following polynomial:

**Possible Answers:**

**Correct answer:**

Begin by extracting from the polynomial:

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

### Example Question #7 : Factoring Polynomials

Factor the following polynomial:

**Possible Answers:**

**Correct answer:**

Begin by rearranging like terms:

Now, factor out like terms:

Rearrange the polynomial:

### Example Question #8 : Factoring Polynomials

Factor the following polynomial:

**Possible Answers:**

**Correct answer:**

Begin by rearranging like terms:

Now, factor out like terms:

Rearrange the polynomial:

Factor:

### Example Question #4 : Factoring Polynomials

Factor the following polynomial:

**Possible Answers:**

**Correct answer:**

Begin by separating into like terms. You do this by multiplying and , then finding factors which sum to

Now, extract like terms:

Simplify: