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P O L Y N O M I A L S

P O L Y N O M I A L S. P O L Y N O M I A L S. Section 6.1. Review. Coefficient: The number in front of the variable. Degree: The sum of the exponents of the variables. ADD THE TOTAL EXPONENTS Term: Parts of an expression that is added or subtracted

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P O L Y N O M I A L S

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  1. P O L Y N O M I A L S P O L Y N O M I A L S Section 6.1 6.1 - Polynomials

  2. Review • Coefficient: The number in front of the variable. • Degree: The sum of the exponents of the variables. ADD THE TOTAL EXPONENTS • Term: Parts of an expression that is added or subtracted • Constant Term: The number at the end of the equation that does not have the variable. • Standard Form:Descending degree form in equation. 6.1 - Polynomials

  3. Degree Examples Identify the total degrees of each monomial. A. z6 B. 5.6 z6 Identify the exponent. 5.6 = 5.6x0 Identify the exponent. The degree is 6. The degree is 0. C. 8xy3 D. a2bc3 8x1y3 Add the exponents. a2b1c3 Add the exponents. The degree is 4. The degree is 6. 6.1 - Polynomials

  4. Definitions • Monomial: A number or a product of numbers and variables with whole numberexponents. • Binomial: A polynomial with two terms • Trinomial: Polynomial with three terms • Polynomial: A monomialorthe sum ordifferenceof monomials. • WHOLE NUMBER DEGREES • 6.1 - Polynomials

  5. a7 1 1 2 2 Is it a Polynomial? • Examples of polynomials: • –3x4 • 0.15x101 • . • Examples of non-polynomials: • . • . • . |2b3 – 6b| m0.75 – m 6.1 - Polynomials

  6. Ranks of Polynomials • Classifying by degree: 6.1 - Polynomials

  7. Ranks of Polynomials Degree Terms 6.1 - Polynomials

  8. Classifying Polynomials Refresh:Standard Form:Descending degree form in equation. Rewrite each polynomial in standard form. Then identify the leading coefficient, HIGHEST degree, and number of terms. Label the polynomial. –5x2 + 4x + 3 1. 3 – 5x2 + 4x Leading coefficient: –5 Write terms in descending order by degree. Highest Degree: 2 Terms: 3 Label: Quadratic Trinomial 6.1 - Polynomials

  9. Classifying Polynomials Refresh:Standard Form:Descending degree form in equation. Rewrite each polynomial in standard form. Then identify the leading coefficient, HIGHEST degree, and number of terms. Label the polynomial. 8x4+ 5x2 + x – 4 2. 5x2 – 4+ 8x4 + x Leading coefficient: 8 Highest Degree: 4 Write terms in descending order by degree. Terms: 4 Label: Quartic with 4 terms Polynomial 6.1 - Polynomials

  10. Quick Examples 2x + 5 • (x + 2) + (x + 3) • x + 2 – x + 3 3. (x2 – 6x + 5) + (3x2 + x – 4) 4. (2x2 + 3x) – (3x2 + x – 4) 5. –3x2 + 5x3 + 2 + 4x2 + x – 8 5 4x2 – 5x + 1 –x2 + 2x + 4 5x3 + x2 + x – 6 6.1 - Polynomials

  11. Add/Subtract Polynomials Keep It Simple, Students Combine like terms when adding or subtracting polynomials 6.1 - Polynomials

  12. Application Example The cost of manufacturing a certain product can be approximated by f(x) = 3x3 – 18x + 45, where x is the number of units of the product in hundreds. Evaluate f(0) and f(200) and describe what the values represent. f(0) = 3(0)3 – 18(0) + 45 = 45 f(200) = 3(200)3 – 18(200) + 45 = 23,996,445 f(0) represents the initial cost before manufacturing any products. f(200) represents the cost of manufacturing 20,000 units of the products. 6.1 - Polynomials

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