This document defines polynomials and describes how to perform basic operations on them: 1) Polynomials are the sum of monomials, where a monomial is a real number, variable, or product of the two. The degree of a polynomial is the highest degree of any term. 2) To add polynomials, combine like terms by adding their coefficients. 3) To subtract polynomials, distribute the negative sign and then combine like terms by subtracting. 4) To multiply polynomials, use distribution and combine like terms by adding.

1. Polynomial Functions Addition, Subtraction, and Multiplication

2. Definitions Monomial – real number, variable, or a product of the two Degree – exponent of the variable Polynomial – a monomial or the sum of monomials. Degree of a polynomial – largest degree of any term of the polynomial

3. Notation Example: P(x) = 2x 3 +3x 2 -x+1 Standard Form of a Polynomial: Polynomial function written in descending order by degree Polynomial function:

4. Adding Polynomials Add coefficients of like terms: Example: Polynomial 4x 2 +2x 3 +13x + x 2 +8x 3 +9 5x 2 Find Common Terms: Add: 5x 2 +10x 3 +13x+9 Standard Form: 10x 3 +5x 2 +13x+9 ( ) ( ) 4x 2 +x 2 +2x 3 +8x 3 +13x +9 +10x 3

5. Subtracting Polynomials Distribute negative sign, find common terms and add/subtract: Example Polynomial (6x 4 -2x 3 -4x 4 )-(x 2 +7x 3 +1) Distribute 6x 4 -2x 3 -4x 4 -x 2 -7x 3 -1 Find Common Terms: Add/Subtract: 2x 4 -9x 3 -x 2 -1 Standard Form: 2x 4 -9x 3 -x 2 -1 6x 4 -4x 4 -2x 3 -7x 3 -x 2 -1 2x 4 -9x 3

6. Multiplying Polynomials Generally distribute and simplify by addition or subtraction Example: +1 ( )(x 2 +5x+6) +1 Multiply: x 3 +5x 2 +6x+x 2 +5x+6 Standard Form: x 3 +6x 2 +11x+6 x (x 2 +5x+6) (x 2 +5x+6) x Polynomial: Distribute: Add Common Terms: x 3 +6 +5x 2 +x 2 +6x +5x +6x 2 +11x