Adding and Subtracting

Polynomials

Monday, March 3, 2014

What are

Mono- is a prefix meaning “one”Bi- is a prefix meaning “two”Tri- is a prefix meaning “three”Poly- is a prefix meaning “many”-nomial is a suffix meaning “terms”Polynomial = Many Terms

Polynomials?

How do we work with

We can perform operations with polynomials (addition, subtraction, multiplication, and division).

When we write polynomials, the standard is to write in descending order of the exponents.

The degree of a polynomial is the highest exponent or sum of the exponents if there are multiple variables.

Polynomials?

Match the polynomial and its degree…

1. 5p2 – 3

2. a3 – 2a2

3. 3 – 6n5 – 8n4

4. -10x4y3 + 6y3 + 4x4y4

A. trinomial degree 8

B. binomial degree 2

C. trinomial degree 5

D. binomial degree 3

Combining Like TermsAdding Polynomials is

really…

Adding the Opposite.Subtracting Polynomials

is really…

Examples:Adding Polynomials

(#1)

(5p2 -3) + (2p2 – 3p3)

Identify like terms and combine them. 5p2 + 2p2 = 7p2

Write in descending order of the exponents.

-3p3 + 7p2 -3

Subtracting Polynomials #(2)

(a3 – 2a2) – (3a2 – 4a3)

Add the opposite, so… (a3 – 2a2) + (-3a2 + 4a3)

Combine like terms… a3 + 4a3 = 5a3 -2a2 + -3a2 = -5a2

5a3 – 5a2

Note: It can be easier if you put

the exponents in order first.

(#16)(-7x5 + 14 – 2x) + (10x4 + 7x + 5x5)

Reorder

-7x5 + 5x5 +10x4 – 2x + 7x + 14

Combine like terms

-2x5 + 10x4 + 5x + 14

Remember, when subtracting,

add the opposite, then reorder.

(#12)(8n – 3n4 + 10n2) – (3n2 + 11n4 – 7)

8n – 3n4 + 10n2 + -3n2 + -11n4 + 7

-3n4 + -11n4 + 10n2 + -3n2 + 8n + 7

Combine like terms

-14n4 + 7n2 + 8n + 7

Practice makes perfect

Classwork –

Adding and Subtracting Polynomials worksheet (1-30)

Practice some more…

Homework –

Adding and Subtracting Polynomials worksheet (1-20)

# 13 and #17-20 are Bonus Problems – Your Exit Ticket is to circle those problems. Please attempt at least one of them.