# Math Refresher — Polynomials

## Polynomials

A polynomial is a collection of terms joined by and operators. Polynomials with one term are called

*monomials,*with two terms is called

*binomial,*with three terms is a

*trinomial,*and so on.

Another (and more important) way to classify a polynomial is by its *degree.* The degree is the value of the highest exponent (power) in the polynomial. For example:

is a second-degree polynomial. Similarly,

is a seventh-degree polynomial.

Finally, each term can be “named” by its exponent. If a term has the exponent 2, it is called the “square” term, exponent 3 is the “cubic” term, exponent 4, the “quartic” term, and so on.

Next we will cover multiplying two binomials.

Got all that? Let’s go…

## Multiplying

Multiplying binomials is taught with an acronymn — FOIL — first, outer, inner, last. How does this work?

- The first terms: are and so their product is

- The outer terms: are and so

- The inner terms: are and so

- The last terms: are and so

Now, sum them all together into the expanded polynomial:

Let’s try some examples.

**Examples.**

- Using the FOIL technique, multiply out
- Use FOIL to multiply

### Squaring

This is a place where students get tripped up. Note that

Here’s the correct way:

Now, FOIL it out, giving:

which equals

**Examples.**

- Square
- Square

### Special cases

You just saw the first special case:

Next, learn this one:

The terms cancel each other, leaving:

So, remember this: the difference of two squares can be factored into

**Examples.**

- Multiply
- Multiply

## Squares and Square Roots

Here’s a good place to mention this. Question: What is ? Immediate answer: 2 !

But that’s not correct. What? The correct answer: Why? Because also.

When you take a square root, always think “”.

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Thanks for these. This is where we are with our Math….

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— Doc