Section 8.1

Adding and Subtracting Polynomials

Standards: A-APR.1 Objective: I will classify polynomials by degree and terms and I will add and subtract polynomials.

Key Words

Key Word Definition & Example

Term An expression that is a number, a variable, or a number with variables.

12 y -5x2y

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x3

Polynomial

An expression made up of one or more terms, separated by addition or subtraction signs.

3x2 – 2x + 5 7x + 6

Key Words

Key Word Definition & Example

Standard Form

A polynomial written in a specific order: ①  exponents from greatest to

least ②  variables in alphabetical

order

5 – 2x 2x + 1 + 3x2

= -2x + 5 = 3x2 + 2x + 1

Classify by Degree: Degree Name Example Exponent

0 1 2 3 4 5 6

constant 3 0 linear -2x + 9 1

quadratic n2 – 4n + 1 2 cubic 12h3 – 5 3

quartic -7y4 + 9y3 4 5th degree 20x5 5 6th degree 11m6 – 8 6

Classify by Terms: Terms Name Example

1 2 3

4 +

monomial binomial 2m8 – 15 trinomial -6z3 – 2z2 + z

polynomial d9 – d8 + d7 – d6

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x34ab

Classify: 2x5 – 5x3 + 4x – 9 degree: term:

-5x2 – 2x3 + 4x degree: term:

x – 2 degree: term:

5th polynomial

cubic trinomial

linear binomial

Key Words

Key Word Definition & Example

Degree of a Monomial

The exponent of the variable in an expression. If there is more than one variable, then add the exponents. 3a3b 3 + 1 = degree 4 12x2y4 2 + 4 = degree 6

Combine like terms using two methods. Adding Polynomials:

Method 1: Add horizontally. Group like terms together, then combine.

Method 2: Add vertically. Rewrite as an addition problem, lining up like terms.

Example: (4x2 + 6x + 7) + (2x2 – 9x + 1) Method 1: Add horizontally.

(4x2 + 2x2) + (6x – 9x) + (7 + 1) 6x2 -3x 8

6x2 – 3x + 8

(2p3 + 6p2 + 4p) + (9p3 – 8p2 + p)

Method 2: Add vertically.

2p3 + 6p2 + 4p 9p3

11p3 – 2p2 + 5p

Example:

+ – 8p2 + p

When you subtract polynomials, distribute the negative sign to each term and change the subtraction sign to an addition sign.

Subtracting Polynomials:

Method 1: Add horizontally.

(2p3 + 3p3) + (6p2 – 8p2) + (4 – 7) 5p3 -2p2 -3

5p3 – 2p2 – 3

(2p3 + 6p2 + 4) – (-3p3 + 8p2 + 7) (2p3 + 6p2 + 4)

Example:

+ (3p3 – 8p2 – 7)