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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
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)