Polynomial Functions

Addition, Subtraction, and Multiplication

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

Notation

Example: P(x) = 2x3+3x2-x+1

Standard Form of a Polynomial: Polynomial function written in descending order

by degree

• Polynomial function:

5x2Find Common Terms:

Adding Polynomials

Add coefficients of like terms:

Example:

Polynomial 4x2+2x3+13x + x2+8x3+9

Add: 5x2+10x3+13x+9

Standard Form: 10x3+5x2+13x+9

( ) ( )

4x2 +x2+2x3 +8x3 +13x +9+10x3

Subtracting Polynomials

Distribute negative sign, find common terms and add/subtract: Example

Polynomial (6x4-2x3-4x4)-(x2+7x3+1)

Distribute 6x4-2x3-4x4-x2-7x3-1

Find Common Terms:

Add/Subtract: 2x4-9x3-x2-1

Standard Form: 2x4-9x3-x2-1

6x4 -4x4 -2x3 -7x3 -x2 -12x4 -9x3

+1( )(x2+5x+6)+1

Multiply: x3+5x2+6x+x2+5x+6

Multiplying Polynomials

Generally distribute and simplify by addition or subtraction

Example:

Standard Form: x3+6x2+11x+6

x (x2+5x+6)(x2+5x+6)xPolynomial:

Distribute:

Add Common Terms: x3 +6+5x2 +x2+6x +5x+6x2 +11x