CLASSIFYING POLYNOMIALS POLYNOMIAL is a sum A or

POLYNOMIAL is a sum A ________ or difference of terms. Polynomials have special names

NAMING BY NUMBER OF TERMS POLYNOMIALS MONOMIALS BINOMIALS TRINOMIALS (1 TERM) (2 TERMS) (3

Classify each polynomial based on the number of terms that it has. Ex. 1:

NAMING BY THE DEGREE The _____ DEGREE of a polynomial is the exponent of

Examples Ex. 5: 5 xy + 9 y 5 Degree: 5 BINOMIAL Ex. 6:

Classify each polynomial above using its degree and number of terms. Ex. 1: 5

Remember how to multiply two binomials by distributing. (aka FOIL) Example: (X+3)(x+1)=(x)(x)+(x)(1)+(3)(x)+(3)((1)

Choose one of these to try! 1. ) (x+2) (x+8) 2. ) (x+5) (x-7)

Check your answers. 1. ) (x+2) (x+8) = X 2+10 x+16 2. ) (x+5)

By learning to use the distributive property, you will be able to multiply any

Choose one of these to try! 1. ) (x 2+x+2) (x+8) 2. ) (x+5)

Check your answers. 1. ) (x 2+x+2) (x+8) = 2. ) (x+5) (3 x

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CLASSIFYING POLYNOMIALS

POLYNOMIAL is a sum A ________ or difference of terms. Polynomials have special names based on their _______ DEGREEand the number of TERMS they have. _______

NAMING BY NUMBER OF TERMS POLYNOMIALS MONOMIALS BINOMIALS TRINOMIALS (1 TERM) (2 TERMS) (3 TERMS)

Classify each polynomial based on the number of terms that it has. Ex. 1: 5 x 2 + 2 x – 4 TRINOMIAL Ex. 2: 3 a 3 + 2 a BINOMIAL Ex. 3: 5 mn 2 MONOMIAL Ex. 4: 3 x 2 MONOMIAL Ex. 5: 4 x 2 – 7 x BINOMIAL Ex. 6: -9 x 2 + 2 x – 5 TRINOMIAL Ex. 7: 5 ab 2 MONOMIAL Ex. 8: -9 a 2 bc 3 – 2 ab 4 BINOMIAL

NAMING BY THE DEGREE The _____ DEGREE of a polynomial is the exponent of the term with the greatest exponent(s). Find the degree of each polynomial below. Ex. 1: 5 x + 9 x 2 Degree: 2 BINOMIAL Ex. 2: 3 x 3 + 5 x – x 2 Degree: 3 TRINOMIAL Ex. 3: -4 x + 7 Degree: 1 BINOMAL Ex. 4: -x 4 + 2 x 2 + 5 x 3 – x Degree: 4 POLYNOMIAL

Examples Ex. 5: 5 xy + 9 y 5 Degree: 5 BINOMIAL Ex. 6: 3 x 3 + 5 xy – x 2 y Degree: 3 TRINOMIAL Ex. 7: -4 xy + 7 y 3 Degree: 3 BINOMIAL Ex. 8: -x 4 + 2 y 7 Degree: 7 BINOMIAL

Classify each polynomial above using its degree and number of terms. Ex. 1: 5 x + 9 x 2 QUADRATIC BINOMIAL Ex. 2: 3 x 3 + 5 x – x 2 CUBIC TRINOMIAL Ex. 3: -4 x + 7 LINEAR BINOMIAL Ex. 4: -x 4 + 2 x 2 + 5 x 3 – x 4 th DEGREE POLYNOMIAL Ex. 5: 5 xy + 9 y 5 5 TH DEGREE BINOMIAL Ex. 6: 3 x 3 + 5 xy – x 2 y 8 TH DEGREE TRINOMIAL Ex. 7: -4 xy + 7 y 3 CUBIC BINOMIAL Ex. 8: -x 4 + 2 y 7 7 TH DEGREE BINOMIAL

Multiplying Polynomials

Remember how to multiply two binomials by distributing. (aka FOIL) Example: (X+3)(x+1)=(x)(x)+(x)(1)+(3)(x)+(3)((1)

Choose one of these to try! 1. ) (x+2) (x+8) 2. ) (x+5) (x-7) 3. ) (2 x+4) (2 x-3)

Check your answers. 1. ) (x+2) (x+8) = X 2+10 x+16 2. ) (x+5) (x-7) = X 2 -2 x-35 3. ) (2 x+4) (2 x-3) = 4 x 2+2 x-12

By learning to use the distributive property, you will be able to multiply any type of polynomials. Example: (x+1)(x 2+2 x+3) = X 3+2 x 2+3 x+x 2+2 x+3

Choose one of these to try! 1. ) (x 2+x+2) (x+8) 2. ) (x+5) (3 x 2 -2 x+7)

Check your answers. 1. ) (x 2+x+2) (x+8) = 2. ) (x+5) (3 x 2 -2 x+7) = x 3+9 x 2+10 x+16 3 x 3+13 x 2 -3 x+35