8-1 ADDING AND SUBTRACTING POLYNOMIALSObjective: to classify, add, and subtract polynomials

What does each prefix mean?

mono one

bitwo

trithree

Vocabulary• We are going to fill in a vocabulary sheet together!

Degree of a Polynomial

• Degree of a monomial: the sum of the exponents of its variables

• Find the degree of each polynomial:

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Classifying Polynomials

Standard Form

• Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms?

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ADDITION:

(4X2 + 5X – 1) + (6X2 – 3X – 4)

4x2 + 5x – 1 + 6x2 – 3x – 4

10x2 + 2x – 5

4x2 + 5x – 1+ 6x2 – 3x – 4 10x2 + 2x – 5

Method 1: Combine Like TermsMethod 2: Like Elimination

TOO1) (6x2y – xy2 + 7) + (-7x2y – 6xy2 – 5)

-x2y – 7xy2 + 22) (x + 6y – 3) + (10y – 3x + 1)

-2x + 16y – 2 3) (7x2 + 5x) + (6 – x)

7x2 + 4x + 6

Method 2: Make sure to line up like termsWrite answer in alphabetical/descending order

SUBTRACTION:

(X2 – 6X + 5) – (3X2 – 5X + 6)**DISTRIBUTE NEGATIVE TO 2ND POLYNOMIAL

x2 – 6x + 5 – 3x2 + 5x – 6

-2x2 – x – 1

x2 – 6x + 5+ -3x2 + 5x – 6 -2x2 – x – 1

Method 1 Method 2

TOO – volunteers to board

1) (6x – xy + 2y) – (-x + 3xy + 5y)

2) (10x2 + 2x + 6) – (6x – 2x2 + 4)

3) (6x – 2) – (10 + 2y)

Find the sum or difference.(5a – 3b) + (2a + 6b)

1. 3a – 9b2. 3a + 3b3. 7a + 3b4. 7a – 3b

Find the sum or difference.(5a – 3b) – (2a + 6b)

1. 3a – 9b2. 3a + 3b3. 7a + 3b4. 7a – 9b

Homework• Pg. 489 # 9 – 47 odd