Notes 4.1 Polynomial Functions
*Polynomial: An algebraic expression that can
be written in the form:
anxn + an-1 xn-1 + …a3x3 + a2x2 + a1x1 + a0
where n is a nonnegative integer, x is a variable,
and each a0, a1, ….an is a constant, called a
coefficient.
*The coefficient a0 is called the constant term.
Characteristics of a Polynomial:
*All exponents are whole #'s
*No variable is contained in a denominator
*No variable is under a radical
Constant Polynomial: A polynomial that consists of
only a constant term.
Zero Polynomial: The constant polynomial zero (0).
Degree of a Polynomial:
• Degree: the exponent of the highest power of
x that appears with nonzero coefficient.
• Nonzero coefficient of this highest power of
the variable is the leading coefficient.
First degree – linear function
Second degree – quadratic function
Third degree – cubic function
Fourth degree – quartic function
Ex. 1 A) Determine if the expression is a polynomial.
If it is, find its B) leading coefficient, C) constant term,
& D) degree.
a) -9
b) 3x
c) –x4 + 3x + 5
• Polynomial Division (My Personal Favorite –
Like LOOOOONNNGGG Division)
• Ex. 2
x – 2 4𝑥 3 − 3𝑥 2 + 𝑥 + 7
Ex. 3
x + 5 3𝑥 3 − 2𝑥 2 − 8