Polynomials

Algebra I

Remember: Monomials are separated by______ or ______ signs.

Monomial = One term – A number, a variable, or a product of numbers and variables.

Binomial = Two terms – 2 monomials separated by a + or – sign.

Trinomial = Three terms – 3 monomials separated by + or – signs.

Identity as a monomial, binomial, trinomial

1) 5x2

2) 4abc

3) 3x + 2

4) 3x2 – 8xy

5) a2 + 2ab + b2

6) 5x2 – 2x + 7

1) Monomial

2) Monomial

3) Binomial

4) Binomial

5) Trinomial

6) Trinomial

To find the degree of a monomial, add the exponents on the variables (from each monomial), then see which one has the largest sum.

7) Largest number is 2

(degree is 2)

8) Largest sum is 8

(degree is 8)

2 0

7 6 4+4=8

27) 3 5x

7 6 4 48) 3y y x m

Do not add across a “+” or “-”

sign!!!!

Remember: Monomials are separated by______ or ______ signs.

5 5 3 6 29) x x y z z 5 5+3+6=14

2

The largest number (sum) is 14, so the degree of this trinomial is 14

Place in ascending order according to (x)

2 310) 5 4 2x x x Ascending means to go

from least to greatest Remember to bring

along sign that is in front of number

Now which terms variable has the smallest exponent?

34x2 x 25x

Place in descending order according to (y)

2 3 2 411) 24 12 6x y x y x Descending means

to go from greatest to least

Remember to bring along sign that is in front of number

Now which terms variable has the largest exponent for “y”?

3 212x y 224x y 46x

12) Write each polynomial in descending (going down) order and give the degree.

2 52 3 3 2x x x 53x 22x 3x 2

5 2 1 0

Largest EXPONENT is 5, therefore the degree is 5.

42x 26 4 0

Largest EXPONENT is 6, therefore The degree is 6.

REMEMBER – look at the exponents on each terms variable,If the term doesn’t have a variable, it’s degree is ZERO.

6 42 3 2x x 63x

13) Evaluate when x = 2 and y = 3.

X2 - 7xy + y2

22 7(2)(3) 2

34 42 9

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