This document summarizes key concepts about polynomials: 1) A polynomial function has exponents that are whole numbers. Functions with non-whole number exponents like y=x^2/3 are not polynomials. 2) The degree of a polynomial is the highest exponent. Constant, linear, quadratic, cubic, and quartic refer to polynomials of degree 0, 1, 2, 3, and 4, respectively. 3) For a polynomial factored into linear factors, the multiplicity or repeated zero is determined by the exponent of the repeated factor.

1. Height of Rocket
Seconds Feet
1 230
2 310
3 350
4 360
5 350
6 300
7 220

2. Section 2.5
Polynomials and
X and Y-intercepts

3. Polynomial Functions
A polynomial function has to have
exponents that are whole numbers
The following are NOT polynomials:
3 2
y 2x 4 x 5x
3
y 3
x
x
y 8

4. Degree and Name
Degree – highest exponent of a
polynomial
Constant
Linear
Quadratic
Cubic
Quartic
Quintic

5. Homework Answers – p106
10. a. r = ks
b. 1.1; r = 1.1s
c. about 45 mi/h
11. b. F(v) = (60/9)v2 or F(v) = 6.67v2
c. 540 N
14. No, there is an exponent that is a variable, not a constant
16. a. d = 1, linear function or polynomial function of degree 1
b. f(6) = 2; f(0) = -7
c. -10
18. d = 3; f(2) = -1

6. Direct Variation Functions
A function that has no translation (shift)
and has some symmetry
Exs.
y = 2x
y = -4x2
y = 3x3
y = -1/2x4

7. Factored Form
3 2
y x 6x 11x 6
y ( x 1)( x 2)( x 3)

8. Graphing from Factored Form
Find the following:
1. zeros (from the factors) and plot them
2. y-intercept (let x = 0)
3. degree to get the end behavior
4. x-values in between zeros to get a
sketch of the graph

9. Graph y = 3x3 – 12x
First, factor the polynomial.
Show x and y intercepts!

10. Multiplicity
A multiple zero is a repeated zero.
Multiplicity is the number of times the
related linear factor is repeated in the
factored form of a polynomial.
– use the exponent of the factor to determine it.
2 3
y ( x 2) ( x 2) ( x 5)

11. Standard form terms are written in descending
order and all “like terms” are combined

12. Writing a polynomial in standard
form.
Example:
y = (x – 1)(x + 2)(x – 4)
What is the degree of the function?

13. Tonight’s Homework
Finish 2.5 class worksheet

14. Warmup – Graph each
2
y x 6x 7
y 2x 5 2
2
y ( x 2) ( x 1)( x 4)

15. Problem of the Day
Simplify:
2 3/2 4 2
(9y ) ( 4y )

16. Sketch the graph of:
y = (x+2)(x-3)(x-3)
Multiple root
or
Multiple zero
Multiplicity = 2