CLASSIFYING POLYNOMIALS. A ___________ is a sum or difference of terms. Polynomials have special names based on their _ and the number of _____.

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Presentation transcript:

CLASSIFYING POLYNOMIALS

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

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

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

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

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

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

Multiplying Polynomials

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

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) = X 2 +10x+16 2.) (x+5) (x-7) = X 2 -2x-35 3.) (2x+4) (2x-3) = 4x 2 +2x-12

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

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

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