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