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3.2

3.2. Introduction to Polynomials. Identify Monomials. Monomial or Term: An expression that is a constant or a product of a constant and variables that are raised to whole number powers. Determine whether the expression is a monomial. 5x -4xy 3 X 6 8.

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3.2

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  1. 3.2 Introduction to Polynomials

  2. Identify Monomials • Monomial or Term: An expression that is a constant or a product of a constant and variables that are raised to whole number powers.

  3. Determine whether the expression is a monomial • 5x • -4xy3 • X6 • 8

  4. Determine whether the expression is a monomial Monomial or Term: An expression that is a constant or a product of a constant and variables that are raised to whole number powers. • 5x • -4xy3 • X6 • 8 • Yes • Yes • Yes • Yes

  5. The following are NOT monomials • 5/xy • 3x2 + 5x – 4 • 9a + 5

  6. Identify the coefficient and degree of a monomial • Two important parts of a monomial are its coefficient and its degree • Coefficient: The numerical factor in a monomial • Degree of a Monomial: The sum of the exponents of all the variables in the monomial

  7. Example Problems • -7x2 • Coefficient: -7 • Degree: 2 • -xy3 • Coefficient: -1 • Degree: 4 • 17 • Coefficient: 17 • Degree: 0

  8. Questions ???

  9. Try Some • M6 • -7x2y3 • 14ab • -10

  10. Answers • M6 • Coefficient: 1 • Degree: 6 • -7x2y3 • Coefficient: -7 • Degree: 5 • 14ab • Coefficient: 14 • Degree: 2 • -10 • Coefficient: -10 • Degree: 0

  11. Identify like terms • Like Terms: Monomials that have the same variables raised to the same exponents. • Note: the definition does not say anything about the coefficient… just the variable and exponent…

  12. Examples • 5x2 and 9x2 • 9xyz and 5xy • 7x2y and 7xy2 • 5a and 9A

  13. Examples • 5x2 and 9x2 • 9xyz and 5xy • 7x2y and 7xy2 • 5a and 9A • YES • NO • NO • NO

  14. You Try… -8x3 and 5x3 12mn and 12m -5y3z and y3z 9t and 12T

  15. Identify polynomials and their terms • Polynomial: A monomial or an expression that can be written as a sum of monomials • Simplest form: An expression written with the fewest symbols possible • Polynomial in one variable: A polynomial in which every variable term has the same variable • Multivariable Polynomial: A polynomial with more than one variable

  16. Some Examples Please • Polynomials: • 2x3 + 5x + 8 • 5x + 7 • 9x3 – 4x2 + 8x – 6 • Simplest form: • 9x3 + (– 4x2) + 8x + (– 6) • 9x3 – 4x2 + 8x – 6  Simplest Form • Both acceptable but we prefer simplest form

  17. More ? .....okay • Polynomial in one variable: • p3 – 5p +2 • 12x3 – 8x + 9 • Multivariable Polynomial: • q3 + 8q3t • 9px2 – 4Px2

  18. Monomials are referred to as terms but polynomials are not because the often have more than one term. In other words polynomials are made of multiple monomials. • Identify the terms in the polynomial and their coefficients: • 9x3– 4x2+ 8x – 6 • First Term: 9x3 Coefficient: 9 • Second Term: - 4x2 Coefficient: - 4 • Third Term: 8x Coefficient: 8 • Fourth Term: - 6 Coefficient: - 6

  19. Monomial: A single-term polynomial Binomial: A polynomial with exactly two terms Trinomial: A polynomial that has exactly three terms Polynomials that have more than three terms have no special name

  20. Identify whether the polynomial is a monomial, binomial, trinomial, or has no special name • 5x3 • - 3x2 + 5x • 4m2 + 6m – 9 • x3 + 4x2 – 9x + 2

  21. Identify the degree of a polynomial • The greatest degree of any of the terms in the polynomial. • 5x3 + 9x6 – 10x2 + 8x – 2 • Degree = 6 • 9x6 has the largest exponent in its term, the degree of the exponent is 6, so 6 is the degree of the polynomial.

  22. Write polynomials in descending order of degree • To write a polynomial in descending order of degree, write the term with the greatest degree first, then the term with the next greatest degree, and so on. • 5x3 + 4x2 – 3x5 – 7 + 9x • - 3x5 + 5x3 + 4x2 + 9x - 7

  23. 9m4 +7m9 – 3m2 + 15m – 6m7 + 2 Your turn…

  24. Practice Worksheet

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