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CLASSIFYING POLYNOMIALS

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

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CLASSIFYING POLYNOMIALS

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  1. CLASSIFYING POLYNOMIALS

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

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

  4. Classify each polynomial based on the number of terms that it has. Ex. 1: 5x2 + 2x – 4 Ex. 2: 3a3 + 2a Ex. 3: 5mn2 Ex. 4: 3x2 Ex. 5: 4x2 – 7x Ex. 6: -9x2 + 2x – 5 Ex. 7: 5ab2 Ex. 8: -9a2bc3 – 2ab4 TRINOMIAL BINOMIAL MONOMIAL MONOMIAL BINOMIAL TRINOMIAL MONOMIAL BINOMIAL

  5. 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 + 9x2 Degree: Ex. 2: 3x3 + 5x – x2 Degree: Ex. 3: -4x + 7 Degree: Ex. 4: -x4 + 2x2 + 5x3 – x Degree: 2 BINOMIAL 3 TRINOMIAL 1 BINOMAL 4 POLYNOMIAL

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

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

  8. Multiplying Polynomials

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

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

  11. 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

  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

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

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

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