ObjectivesObjectivesWe must be able to :We must be able to :

Analyze the given term whether its POLYNOMIAL or NOT POLYNOMIAL.Analyze the given term whether its POLYNOMIAL or NOT POLYNOMIAL. Identifying the degree of a polynomial.Identifying the degree of a polynomial.

What does each prefix What does each prefix mean?mean?

monomono one

bitwo

trithree

What about poly?What about poly?

one or moreone or more

A A polynomialpolynomial is a monomial or a is a monomial or a sum/difference of monomials.sum/difference of monomials.

An expression is An expression is not a polynomial not a polynomial if if there is a variable in the denominator.there is a variable in the denominator.

POLYNOMIAL OR NOT POLYNOMIAL OR NOT POLYNOMIALPOLYNOMIAL

1) 7y - 3x + 41) 7y - 3x + 4

trinomialtrinomial

2) 10x2) 10x33yzyz22

monomialmonomial

3) 3X-X⅞3) 3X-X⅞

not a polynomialnot a polynomial

RULESRULES If a term in a polynomial has one variable as a If a term in a polynomial has one variable as a

factor, then the degrees of that term is the factor, then the degrees of that term is the power of the variable.power of the variable.

If two or more variables are present in term as a factor, the degree of the term is the sum of the power of the variables.

The degree of a polynomial is the greatest degree of any term in a polynomial.

Any non-zero constant is defined to be a polynomial of degree zero.

The The degreedegree of a monomial is the sum of a monomial is the sum of the exponents of the variables.of the exponents of the variables.

1) 5x1) 5x22

22

2)2) 4a4a44bb33cc

88

3)3) -3-3

00

To find the degree of a polynomial, To find the degree of a polynomial, find the find the largest degree largest degree of the of the

terms.terms.

1) 8x2 - 2x + 7

Degrees: 2 1 0

Which is biggest? 2 is the degree!

2) y7 + 6y4 + 3x4m4

Degrees: 7 4 8

8 is the degree!

x 0

2

1

xx

Not a polynomial because of the square root since the power is NOT an integer

xxxf 42

Determine which of the following are Determine which of the following are polynomial functions. If the function is a polynomial functions. If the function is a

polynomial, state its degree.polynomial, state its degree.

A polynomial of degree 4.A polynomial of degree 4.

2xg

12 xxh

23x

xxF

A polynomial of degree 0.

We can write in an x0 since this = 1.

Not a polynomial because of the x in the denominator since the power is negative

11 xx

PREPARED BY :PREPARED BY :

Alay,Helen Grace A.Alay,Helen Grace A.

0930201209302012