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

Leading coefficient

The degree of a polynomial is the largest exponent.

This is a polynomial of degree 3.

12x – 8x2 + 6

Classifying Polynomials

Polynomial Degree # Degree Name Name by Numberof terms

6 0 constant monomial

-2x 1 linear monomial

3x + 1 1 linear binomial

-x2 + 2x – 5 2 quadratic trinomial

4x3 – 8x 3 cubic binomial

2x4 – 3x2 + 4x – 7 4 quartic polynomial

Terms Name 1 2 3 >3

Degree Name 0 1 2 3

Monomial Constant Binomial

TrinomialPolynomial

Linear Quadratic

Cubic

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

What is the leading coefficient? -10

Classify this polynomial by degree.

Cubic

Adding Polynomials

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

Answer: 7x2 - 2+ x

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

Answer: -11x3 - x+ 3x2 + 5

Classify this polynomial by the number of terms.

Trinomial

What is the leading coefficient? -11

Subtracting Polynomials

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

(-6x3 + 5x – 3) + (-2x3 – 4x2 + 3x – 1)

Answer: -8x3 + 8x- 4x2

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

Answer: + 215x

- 4

(12x – 8x2 + 6) + (8x2 + 3x – 4)

Classify this polynomial by degree.

Linear

Classify this polynomial by the # of terms.

Binomial

HW

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