# ISEE Upper Level Math : Variables and Exponents

## Example Questions

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### Example Question #1 : Variables And Exponents

Rewrite the polynomial in standard form:

Explanation:

The degree of a term of a polynomial with one variable is the exponent of that variable. The terms of a polynomial in standard form are written in descending order of degree. Therefore, we rearrange the terms by their exponent, from 5 down to 0, noting that we can rewrite the  and constant terms with exponents 1 and 0, respectively:

Simplify:

Explanation:

### Example Question #3 : Variables And Exponents

Assume that . Simplify:

Explanation:

If , simplify:

Explanation:

If , simplify:

Explanation:

### Example Question #6 : Variables And Exponents

Define

What is  ?

Explanation:

Substitute  for  in the definition:

Explanation:

### Example Question #8 : Variables And Exponents

Simplify:

Explanation:

We can expand the first term using FOIL:

Reorder the expression to group like-terms together.

Simplify by combining like-terms.

### Example Question #9 : Variables And Exponents

Simplify:

Explanation:

Expand each term by using FOIL:

Rearrange to group like-terms together.

Simplify by combining like-terms.

Simplify: