CLASSIFYING POLYNOMIALS

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: 5x2 2x – 4 TRINOMIAL Ex. 2: 3a3 2a BINOMIAL Ex. 3: 5mn2 MONOMIAL Ex. 4: 3x2 MONOMIAL Ex. 5: 4x2 – 7x BINOMIAL Ex. 6: -9x2 2x – 5 TRINOMIAL Ex. 7: 5ab2 MONOMIAL Ex. 8: -9a2bc3 – 2ab4 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: 5x 9x2 Degree: 2 BINOMIAL Ex. 2: 3x3 5x – x2 Degree: 3 TRINOMIAL Ex. 3: -4x 7 Degree: 1 BINOMAL Ex. 4: -x4 2x2 5x3 – x Degree: 4 POLYNOMIAL

Examples Ex. 5: 5xy 9y5 Degree: 5 BINOMIAL Ex. 6: 3x3 5xy – x2y Degree: 3 TRINOMIAL Ex. 7: -4xy 7y3 Degree: 3 BINOMIAL Ex. 8: -x4 2y7 Degree: 7 BINOMIAL

Classify each polynomial above using its degree and number of terms. Ex. 1: 5x 9x2 QUADRATIC BINOMIAL Ex. 2: 3x3 5x – x2 CUBIC TRINOMIAL Ex. 3: -4x 7 LINEAR BINOMIAL Ex. 4: -x4 2x2 5x3 – x 4th DEGREE POLYNOMIAL Ex. 5: 5xy 9y5 5TH DEGREE BINOMIAL Ex. 6: 3x3 5xy – x2y 8TH DEGREE TRINOMIAL Ex. 7: -4xy 7y3 CUBIC BINOMIAL Ex. 8: -x4 2y7 7TH 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) x 2 x 3x 3 2 x 4x 3

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

Check your answers. 1.) (x 2) (x 8) X2 10x 16 2.) (x 5) (x-7) X2-2x-35 3.) (2x 4) (2x-3) 4x2 2x-12

By learning to use the distributive property, you will be able to multiply any type of polynomials . Example: (x 1)(x2 2x 3) (x 1)(x2 2x 3) X3 2x2 3x x2 2x 3 x 3 3x 2 5x 3

Choose one of these to try! 1.) (x2 x 2) (x 8) 2.) (x 5) (3x2-2x 7)

Check your answers. 1.) (x2 x 2) (x 8) 2.) (x 5) (3x2-2x 7) x3 9x2 10x 16 3x3 13x2-3x 35