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What is a polynomial?

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

​Note taking Guide

Video Guide

0:38 Adding polynomials.(-3x^2+4y-9) + (2-y-7x^2)
 Remember that you can only add like terms.

1:30 This problem involves subtraction of polynomials. 
(4z-6)- (4x^2-2z+4)

3:02 Write a polynomial that represents perimeter.

4:50 Find the product of....
4a^3(a^2-5a^2-2a)

6:28 Find the product of a binomial
(5x+1)(x-8)
This problem uses the FOIL method to solve this problem.

8:07 This problem involves a binomial times a trinomial
(n+1)(n^2+4n + 5)

10:51 Solves (x-4)(x+5)-2x^2(x-1)
Involves a binomial times a binomial and then monomial times a binomial

12:42 Binomial times a binomial 
(m-2)(m-3) + (m-5)(m+5)