Polynomials

(1) Adding and Subtracting Polynomials

(2) Multiplying Polynomials

(3) Factoring Quadratic Equations

There are two important things to remember about adding polynomials.

1) Add Like Terms - Like terms are monomials that have the exact same variable(s) with the exact same exponent(s). Like terms are combined by adding the coefficients.

2) Subtraction = Change All the Signs - If you are subtracting a polynomial then you change the subtraction to addition and then change all the signs of the polynomial that was being subtracted. For example:

(2x2 + 3x - 7) - (4x2 - 2x + 3)

Is rewritten as:

2x2 + 3x - 7 - 4x2 + 2x - 3

Notice how the parenthesis are removed after we deal with the subtraction.

The following video shows three examples how to add and subtract polynomials.

There are multiple different methods that are taught to students trying to learn how to multiply binomials together. FOIL, the smiley face method, and double distributive property are a few of them. All of these are valid ways to multiply binomials, but we are going to discuss double distributive property because it works for more difficult properties as well.

Double Distributive Property

The double distributive property describes the process of multiplying two binomials together. It works like this:

1) Multiply the first term of the first binomial times the two terms of second binomial.

2) Multiply the second term of the first binomial times the two terms in the second binomial.

3) Add like terms.

The good thing about learning it this way is that it is easy to extend the method to more complex problems. For example if you are multiplying two trinomials:

1) Multiply the first term of the first trinomial times all three terms in the second trinomial.

2) Multiply the second term of the first trinomial times all three terms in the second trinomial.

3) Multiply the third term of the first trinomial times all three terms in the second trinomial.

4) Add like terms.

The following videos show examples of multiplying various polynomials together.

As with multiplying binomials there are various methods for factoring quadratic equations. The following videos illustrate the "guess and check" method of factoring quadratics. I like to teach this method because it helps students understand the "why" of factoring. The other methods are more "magic" and don't teach as much for understanding.

The only special case I teach is the difference of two squares. There are a couple of examples of how that works as well.