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5.5 Polynomials

5.5 Polynomials. Goals: To identify terms, coefficients, and factors of a term. To simplify a poly by collecting like terms To identify the degree of the poly. Mono__________________ Bi______________________ Tri_____________________ Poly______________________. Monomial  Polynomials.

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5.5 Polynomials

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  1. 5.5 Polynomials • Goals: • To identify terms, coefficients, and factors of a term. • To simplify a poly by collecting like terms • To identify the degree of the poly

  2. Mono__________________ Bi______________________ Tri_____________________ Poly______________________

  3. Monomial  Polynomials A Polynomial is a monomial, or a sum of monomials 3x2 + 2x - 5 5x + 3 Trinomial Binomial

  4. To determine if an expression is a polynomial:First check that every term is a monomial. If every term is a monomial then the expression is a polynomial

  5. Is the term a polynomial? If so, say whether it is a monomial, binomial, or trinomial. y2 + 2y Binomial, since it has two TERMS “terms” are added, “factors” are multiplied

  6. Is the term a polynomial? If so, say whether it is a monomial, binomial, or trinomial. No “terms” are added, “factors” are multiplied

  7. Is the term a polynomial? If so, say whether it is a monomial, binomial, or trinomial. YES, trinomial since it has 3 terms Numeric factor of a term is called the coefficient.

  8. To simplify by collecting “like terms” “like terms” have the same exact variables to the same exact power. Only the coefficients may be different. 7m2 – 2m2 = (7 – 2)m2 = 5m2

  9. To simplify by collecting “like terms” “like terms” have the same exact variables to the same exact power. Only the coefficients may be different. 3x5y4– 6y4 – x5y4 + 2y4 +(– 6 + 2) y4 = (3 – 1)x5y4 = 2x5y4 - 4y4

  10. Simplify by collecting like terms: 2m4 – 4m3 + 3m3 – 1 2m4 – m3 – 1

  11. Simplify by collecting like terms: 3m5 – 3m2 + m – 1 (no like terms)

  12. Simplify by collecting like terms: 3x5y4 – 6y4 + m3 – x5y4 2x5y4 – 6y4 + m3 9th deg 3rd deg 4th deg The Degree of a termis the sum of the exponents of the variables.

  13. Simplify by collecting like terms: 3x5y4 – 6y4 + m3 – x5y4 2x5y4 – 6y4 + m3 This is a 9th degree polynomial. The Degree of a termis the sum of the exponents of the variables. The Degree of a polynomialis the highest degree of any term.

  14. Identify the degree of each term and the degree of the polynomial. - 63x2y3 – 16xy5 + y4 6th deg 5th deg 4th deg This is a 6th degree polynomial. The Degree of a termis the sum of the exponents of the variables. The Degree of a polynomialis the highest degree of any term.

  15. Identify the degree of each term and the degree of the polynomial. 9x6y5 – 7x4y3 + 3xy4 7th deg 11th deg 5th deg This is a 11th degree polynomial. The Degree of a termis the sum of the exponents of the variables. The Degree of a polynomialis the highest degree of any term.

  16. 9x6y5 – 7x4y3 + 3xy4 • Leading term is the term that has the highest degree in the poly • Ex: 9x6y5 • Leading coefficient is the coefficient of the leading term. • Ex: 9

  17. Assignment: Page 224 6-46 even

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