Polynomials are simply algebraic expressions. These expressions can contain whole numbers and variables with multiplication, addition, and subtraction.

The variables cannot contain:

Negative exponents

Square roots (which are fractional exponents)

Fractional exponents

There are three major polynomials you will be working with most often.

Monomial contain one term. For example: 5x or 6 or 6x^2

Binomial contain two terms. For example: (5x+6), (3x^2-5y)

Trinomial contain three terms. For example: (5x^2+6-6x) or (x^2+4x-2)

Adding Polynomials

Add (3x^2 -6) + (x^2 +4x -2)

Remove parentheses

3x^2 - 6 + x^2 + 4x - 2

Identify like terms

3x^2 - 6 + x^2 + 4x - 2

Group and add like terms

3x^2 + x^2 + 4x - 6 - 2

Final answer: 4x^2 + 4x - 8

Subtracting Polynomials

Subtracting polynomials is very similar to adding polynomials except for one step.

Subtract

(3x^2 - 5) – (x^2 + 4x - 6)

For all terms being subtracted change their signs and change any addition signs to subtraction by distributing the negative to the 2nd polynomial.

(3x^2 - 5) + -x^2 - 4x + 6

Remove parentheses

3x^2 - 5 + -x^2 - 4x + 6

Identify like terms

3x^2 - 5 + -x^2 - 4x + 6

Group and add like terms

3x^2 - x^2 - 4x - 5 + 6

2x^2 - 4x +1

Multiplying Polynomials

When multiplying polynomials the method that works for all types polynomials is the “Distributive Method “

When you distribute an exponent remember to add the exponents , but multiply the coefficients.

Multiplying a Polynomial example 1

Multiplying a Polynomial example 2

When you distribute a binomial you can FOIL the expression

Adding, Subtracting,Multiplying Polynomials Video Tutorials