Definition of Polynomial Functions
function of the form
with a ≠ 0, is called a polynomial function of degree n. The
numbers
are the coefficients of the function .
Naming Polynomials
We use the notation
Example
P(x) = 5x3 − x2 + 3x − 1
P(−2) = 5(−2)3 − (−2)2 + 3(−2) − 1
= 5(−8) − 4 − 6 − 1
= −51
Addition and Subtraction of Polynomials
Remove parentheses
Combine like terms
Example
(−x2 + 3x − 1) − (6x2 + 4x − 5) = −x2 + 3x − 1 − 6x2 − 4x
+ 5
= −7x2 − x + 4
Multiplication of Polynomials
FOIL method
Distributive property
Special Products
(a − b)2 = a2 − 2ab + b2
(a + b)2 = a2 + 2ab + b2
(a − b)(a + b) = a2 − b2
Example
(2z − 3)(2z + 3) = (2z)2 − 32
= 4z2 − 9
(3x − 1)(x + 4) = 3x2 + 11x − 4
Division of Polynomials
Use long division to divide 2x3 − 7x + 1 by 2x2 − 1.
Use long division to divide 4x3 − 2x2 + 1 by x − 2.
