# Algebra II : Polynomials

## Example Questions

### Example Question #1 : Factoring Polynomials

Factor the following expression:

Explanation:

To factor, we are looking for two terms that multiply to give  and add together to get .

Possible factors of :

Based on these options, it is clear our factors are  and .

### Example Question #13 : Factoring Polynomials

Factor the following expression:

Explanation:

To factor, we are looking for two terms that multiply to give  and add together to get .

Possible factors of :

Based on these options, it is clear our factors are  and .

### Example Question #14 : Factoring Polynomials

Factor the following expression:

Explanation:

To factor, we are looking for two terms that multiply to give  and add together to get .

Possible factors of :

Based on these options, it is clear our factors are  and .

### Example Question #1 : Factoring Polynomials

Factor the following expression:

Explanation:

To factor, we are looking for two terms that multiply to give  and add together to get . There are numerous factors of , so we will only list a few.

Possible factors of :

Based on these options, it is clear our factors are  and .

### Example Question #16 : Factoring Polynomials

Factor the following expression:

Explanation:

To factor, we are looking for two terms that multiply to give  and add together to get . There are numerous factors of , so we will only list a few.

Possible factors of :

Based on these options, it is clear our factors are  and .

### Example Question #12 : Factoring Polynomials

Factor the following expression:

Explanation:

To factor, we are looking for two terms that multiply to give  and add together to get .

Possible factors of :

Based on these options, it is clear our factors are  and .

### Example Question #18 : Factoring Polynomials

Simplify:

Explanation:

Factor the numerator:

Simplify the fraction:

### Example Question #21 : Factoring Polynomials

Factor:

Explanation:

Factor:

Step 1: Factor out

Step 2: Factor the polynomial

### Example Question #21 : Factoring Polynomials

Factor:

Explanation:

Factor:

When factoring a polynomial , the product of the coefficients must be , the sum of the factors must be , and the product of the factors must be .

For the above equation, , , and .

Set up the factor equation:

Becauase is negative, one of the factors must be negative as well.  Because is positive, this means the larger factor is positive as well.

Two numbers that meet these requirements are and .  Their product is , and their sum is .

### Example Question #23 : Factoring Polynomials

Expand:

Explanation:

Follow the FOIL rule when multiplying - first, outside, inside, last.

First:

Oustide:

Inside:

Last:

Combine like terms: