POLYNOMIALS REVIEW

Classifying PolynomialsAdding & Subtracting Polynomials

Multiplying Polynomials

Remember: Monomials are separated

by _____ or _____ signs.

But, what is a monomial?

A number or variable or product of numbers and variables.

5x2 6 x

- y2z3 ½xy

“Poly” means _________________?

Polynomials can be classified according to the number of terms they have.

• ONE TERM – • TWO TERMS – • THREE TERMS -

5 5 3 6 2x x y z z Classify the following:

3x2 – 8xy4abc

3x2 – 8xy

5x2

a2 + 2ab + b2

DEGREE………………The degree of a monomial is

determined by adding the exponents of its variables.

So, to find the degree of a POLYnomial, find the degree of each separate MONOmial. The Monomial with the HIGHEST sum determines the degree of the problem.

5 5 3 6 2x x y z z

23 5x

7 6 4 43y y x m

Ascending & Descending Order

• Ascending – means to count up! So, order the VARIABLES exponents

from least to greatest.

• Descending – means to count down! So, order the VARIABLES exponents

from greatest to least.

2 35 4 2x x x 3 24 5 2x x x

2 3 2 424 12 6x y x y x 3 212x y 224x y 46x

2 35 4 2x x x 34x2 x 25x2 3 2 424 12 6x y x y x 2 3 2 424 12 6x y x y x

( of “y” )

22 5 8x y

2033 8 2x y

6

Adding & SubtractingPolynomials

2(3 5 6)y y 2(7 9)y 210y 5y 15

2 2(3 3 )a ab b 2(4 6 )ab b 23a 7ab 25b

2(3 2)x (9x 1) 2(7x 4 )x210 5 1x x

2 2(4 3 5 )x y xy (8xy 26x 23 )y2 22 3 6x xy y

Subtract 28 5x x from

22 6x x23x 2x 5

4(8 6)x 2(4x 2) 4(2x 2 )x4 210 5 8x x

Multiplying Polynomials34 (3 3 )x x y

412 12x xy 45 (8 5 )x x y 540x 25 4x y

4 3 23 (2 4 4 6)x x x x 6 7x 12 6x 12 5x 18 4x

2 2 36 ( 4 2 )x y x xy y 46x y 3 224x y 2 412x y

2 2 32 ( 4 7 )x y x xy y 42x y 3 28x y 2 414x y

( 7)( 1)x x 2x 8x 7

( 4)( 2)x x 2x 6x 8

( 6)( 5)x x 2x 11x 30

( 7)( 3)x x 2x 10x 21( 9)( 3)x x

2x 6x 27

( 6)( 3)x x 2x 3x 18

( 1)( 8)x x 2 7 8x x

( 2)( 7)x x 2 5 14x x

Tie Breaker

(3x + 2) (2x + 3)

6x2 + 13x + 6