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### Algebra

10.1 Adding and Subtracting Polynomials

Intro

- Polynomial-the sum of terms in the form axk where k is a nonnegative integer.
- A polynomial is usually written in standard form meaning the terms are placed in descending order by degree(exponent).
-4x3 + 5x2 – 4x + 9

12x – 8x2 + 6

The degree of a polynomial is the largest exponent.

Leading coefficient

This is a polynomial of degree 3.

TermsName

1

2

3

>3

Binomial

Monomial

DegreeName

0

1

2

3

Classifying PolynomialsConstant

Linear

Trinomial

Polynomial

Quadratic

Cubic

Name by Number

of terms

Degree #

Degree Name

Polynomial

0

constant

monomial

6

1

linear

monomial

-2x

1

linear

3x + 1

binomial

quadratic

trinomial

-x2 + 2x – 5

2

3

cubic

4x3 – 8x

binomial

quartic

polynomial

2x4 – 3x2 + 4x – 7

4

Writing a Polynomial in Standard Form

- Let’s try: 4x – 3x3 + 2x2 – 9
Standard form: -3x3 + 2x2 + 4x – 9

- You try: -9x + 3 + 4x2 – 10x4
Standard form: -10x4 + 4x2 – 9x + 3

Classify this polynomial by degree.

Cubic

-10

What is the leading coefficient?

Adding Polynomials

Let’s try: (6x2 – x + 3) + (-2x + x2 – 7) + (4x + 2)

Answer:

7x2

+ x

- 2

Trinomial

Classify this polynomial by the number of terms.

You try: (-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3)

-11

What is the leading coefficient?

Answer:

-11x3

+ 3x2

- x

+ 5

Subtracting Polynomials

Let’s try: (-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1)

(-6x3 + 5x – 3) + (-2x3– 4x2+ 3x – 1)

Answer:

-8x3

- 4x2

+ 8x

- 4

You try: (12x – 8x2 + 6) – (-8x2 – 3x + 4)

(12x – 8x2 + 6) + (8x2+ 3x – 4)

Answer:

15x

+ 2

Classify this polynomial by degree.

Classify this polynomial by the # of terms.

Linear

Binomial

HW

- P. 579 – 580 (13-29 odd, 53-60, 73-78)

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