# Algebra II : Polynomials

## Example Questions

### Example Question #31 : Simplifying Polynomials

Simplify the polynomial.  Assume that no variable equals zero.

Explanation:

It is important to remember that ;

### Example Question #31 : Simplifying Polynomials

Simplify:

Explanation:

To simplify this expression, first identify what all the terms have in common. In this case, it's 2x. Now, factor that out from each of the terms to get your answer: .

### Example Question #33 : Simplifying Polynomials

Simplify:

Explanation:

To simplify, first use the distributive property: . Then, combine like terms to get your answer: .

### Example Question #34 : Simplifying Polynomials

Put the following polynomial into standard form:

Explanation:

### Example Question #35 : Simplifying Polynomials

Write the polynomial in standard form that has zeroes at 3, and .

Explanation:

From the zeroes we know:

First use FOIL method to simplify terms containing irrational numbers:

Which simplifies to:

FOIL again:

### Example Question #36 : Simplifying Polynomials

Simplify .

Explanation:

We can start by factoring a  out of the numerator and denominator and cancel them:

Then we can factor the quadratic that's left in the denominator and cancel the one of the terms with the term in the numerator:

### Example Question #37 : Simplifying Polynomials

If  and , simplify .

Explanation:

We should start by writing everything out so we can have a good look at it:

To factor the numerator, let's group the first two and the last two terms:

We can factor out a  from the first group in the numerator, and a  from the second group:

Now we can factor out the  from both terms in the numerator:

We can then cancel the  from the numerator and the denominator, leaving us with a final answer of:

### Example Question #38 : Simplifying Polynomials

Simplify the polynomial:

Explanation:

To simplify the polynomial expression, we can simplify each term individually. To start, the first term has a difference of squares in the numerator, which can be rewritten as

using the formula

We can now simplify the first term completely to .

The second term can now be simplified:

Note that one could also simplify the denominator by itself by finding the least common denominator, and then simplify the entire term.

Now that all the terms are simplified, our final answer is

### Example Question #39 : Simplifying Polynomials

Simplify:

Explanation:

To simplify this expression, identify what goes into every one of the terms.

In this case, it's -7.

Then, take that out from each of the terms, remembering to pay attention to the signs.

.

Simplify: