Transcript Polynomial Functions Addition, Subtraction, and Multiplication

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
• Polynomial function:
Example: P(x) = 2x3+3x2-x+1
Standard Form of a Polynomial:
Polynomial function written in descending order
by degree
Adding Polynomials
Add coefficients of like terms:
Example:
Polynomial
(4x2+2x3+13x)+(x2+8x3+9)
4x2 +10x
+2x3 3+13x+x2 +8x3 +9
Find Common Terms: 5x
Add:
5x2+10x3+13x+9
Standard Form:
10x3+5x2+13x+9
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
3-4x
3 4 -x2 -7x3 -1
2x4 -2x
-9x
Find Common Terms: 6x
Add/Subtract:
2x4-9x3-x2-1
Standard Form:
2x4-9x3-x2-1
Multiplying Polynomials
Generally distribute and simplify by
addition or subtraction
Example:
Polynomial:
(x +1)(x
(x22+5x+6)
+5x+6)
Distribute:
Multiply:
x3+5x2+6x+x2+5x+6
Add Common Terms: x3 +5x
+6x2+6x
+11x
+x2 +5x +6
Standard Form:
x3+6x2+11x+6