1. Warm-Up 4 minutes Evaluate each expression for x = -2. 1) -x + 1
Simplify each expression.
4) (x + 5) + (2x + 3)
5) (x + 9) – (4x + 6)
6) (-x2 – 2) – (x2 – 2)

2. 5.1 An Intro to Polynomials
Objectives:
Identify, evaluate, add, and subtract polynomials
Classify polynomials, and describe the shapes of their graphs

3. Classification of a Polynomial
Degree
Name
Example
n = 0
constant 3
n = 1
linear
5x + 4
n = 2
quadratic
2x2 + 3x - 2
n = 3
cubic
5x3 + 3x2 – x + 9
n = 4
quartic
3x4 – 2x3 + 8x2 – 6x + 5
n = 5
quintic
-2x5 + 3x4 – x3 + 3x2 – 2x + 6

4. Example 1 Classify each polynomial by degree and by number of terms.
a) 5x + 2x3 – 2x2
cubic trinomial
b) x5 – 4x3 – x5 + 3x2 + 4x3
quadratic monomial

5. Example 2
Add
(5x2 + 3x + 4) + (3x2 + 5)
= 8x2
+ 3x
+ 9

6. Example 3 -3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1 5x5 - 3x3y3 - 5xy5 5x5
Add
(-3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1) + (5x5 – 3x3y3 – 5xy5)
-3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1
5x x3y xy5
5x5
– 3x4y3
+ 3x3y3
– 6x2
+ 1

7. Example 4 Subtract. (2a4b + 5a3b2 – 4a2b3) – (4a4b + 2a3b2 – 4ab)

8. Example 5
If the cubic function C(x) = 3x3 – 15x + 15 gives the cost of manufacturing x units (in thousands) of a product, what is the cost to manufacture 10,000 units of the product?
C(x) = 3x3 – 15x + 15
C(10) = 3(10)3 – 15(10) + 15
C(10) = 3000 –
C(10) = 2865
$2865