A polynomial function is a function of the form
Where a x n n + a
n – 1 x n –
1 +· · ·+ a
1 x + a
0 a
0

0 and the exponents are all whole numbers.
For this polynomial function, a a a
0 0
A polynomial function is in standard form if its terms are

You are already familiar with some types of polynomial functions. Here is a summary of common types of polynomial functions.
Degree
2
3
4
0
1
Type
Constant
Linear
Quadratic
Cubic
Quartic
Standard Form
f (x) = a
0
f (x) = a
1 x + a
0
f (x) = a
2 x 2 + a
1 x + a
0
f (x) = a
3 x
3
+ a
2 x
2
+ a
1 x + a
0
f (x) = a
4 x 4 + a
3 x 3 + a
2 x 2 + a
1 x + a
0

One Variable Polynomial, Degrees and Leading
Coefficients a.) f 𝑧 = 7𝑧 3 − 4𝑧 2 + 𝑧 b.) w x = 2𝑥 5 + 3𝑥 2 − 4 − 8𝑥 6 c.) 𝜎 𝑥 = 6𝑥 2 + 2𝑥 −1 + 𝑥 d.) 𝑔 𝑏 = 𝑥 4 𝑦 + 3 𝑥 e.) 𝑓 𝑥 = 𝑥 3 + 𝜋𝑥 − 2

Function Values of Variables a.) Find 𝑔 −𝑏 + 3𝑔 2𝑏 if 𝑔 𝑥 = 3𝑥 − 10.
b.) Find 𝑓 2𝑎 − 1 if 𝑓 𝑥 = 2𝑥 2 + 𝑥 − 1.

Zeros of Even- and Odd-Degree Functions
Odd-Degree functions will always have an odd number of real zeros.
Even-Degree functions will always have an even number of real zeros or no real zeros at all.

For the graph,
• Describe the end behavior,
• Determine if it’s Odd or Even-degree
• State the number of zeros.

Assignment
Pg. 326-327
#17-39 odd