Lesson 5-1/5-2Polynomials &

Adding/Subtracting

ObjectiveStudents will:Evaluate polynomial functionsSimplify polynomials by collecting like termsAdd/Subtract polynomialsFind the additive inverse of polynomials

Polynomials

A collection of terms:

2x 3x – 4 x3 – 2x2y + 8

Coefficients: numbers in front of each term

Degree of a term: sum of exponents acting on the variables

Degree of polynomials: equal to highest degree of any term

Names: monomial, binomial, trinomial

General form (descending order):

anxn + an-1xn-1 + …+ a1x + a0

Polynomial Functions: Evaluate by plugging in

P(x) = x2 – 5x + 8 when x = 6

P(6) = 62 – 5(6) + 8 = 14

Simplifying Polynomials: combine like terms (same variable parts)

Example 1 Simplify, state the degree, and give the specific name.

2x2y – 4x + 4y – 3xy2 + x

2x2y – 3xy2 – 3x + 4y

Degree: 3 (x2y1= 2+1) Name: More than 3 terms so just polynomial will do!

Adding/Subtracting Polynomials

Combine like terms:

A) Mark like terms

Or

B) line up vertically

Additive Inverse: Polynomial with all opposite terms

EX: 2x2 -3x + 5 Additive inverse: -2x2 + 3x -5

When problem is subtraction, Change to add the inverse!!!

Example 2 Subtract (change to additive inverse)

Method A) Mark LikeTerms

(4xy2 – 6x2y2 + 5x3y2) – (2xy2 + 4x2y2 – 8x3y2)

(4xy2 – 6x2y2 + 5x3y2) + (-2xy2 - 4x2y2 + 8x3y2)

2xy2 - 10x2y2 + 13x3y2)

Example 2 Subtract (change to additive inverse)

Method B) Line up Vertically

(4xy2 – 6x2y2 + 5x3y2) – (2xy2 + 4x2y2 – 8x3y2)

(4xy2 – 6x2y2 + 5x3y2)

+ (-2xy2 - 4x2y2 + 8x3y2)

2xy2 - 10x2y2 + 13x3y2

You Try(5xy4 - 7xy2 + 4x2 - 3) – (-3xy4 + 2xy2 - 2y + 4)

Assignment

5-1/208 / 3- 31 eoo, 41-49o

5-2/ 212-213/1-29 eoo, 37, 45