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Monomials

Monomials. An expression that is either a number, a variable, or a product of numerals and variables with whole number exponents. Monomials. 5x 3 y 12 is a monomial is not a monomial is not a monomial. Vocabulary. Constants monomials that contain no variables

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Monomials

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  1. Monomials An expression that is either a number, a variable, or a product of numerals and variables with whole number exponents.

  2. Monomials 5x3y12 is a monomial is not a monomial is not a monomial

  3. Vocabulary • Constants monomials that contain no variables Example 3 or -22 • Coefficient Numeric factor of the term -32x3y12z15 coefficient = -32

  4. Vocabulary (continued) • Degree of a Monomial The sum of the exponents of the variables 3x4 degree = 4 -32x3y12z15 degree = 3+12+15 = 30 5 degree = 0

  5. Vocabulary (continued) • Power An expression in the form of xn Can also refer to the exponent

  6. Product of Powers • For any real number a and integers m and n, am · an =am+n 23 · 25 =2 · 2 · 2 · 2 · 2 · 2 · 2 · 2= 28

  7. Quotient of Powers • For any real number a and integers m and n,

  8. Quotient of Powers • Find the quotient

  9. NEGATIVE EXPONENTS • For any real number a≠0 and any integer n, a-n=

  10. Vocabulary (continued) Simplify rewrite expression • No parenthesis • No negative exponents • Multiply variables • Combine like terms

  11. Simplify (-2a3b)(-5ab4) • Multiply Coefficients (-2)(-5)=10 • Multiply Variables (a3)(a) = a4 (b)(b4) = b5 • 10a4b5

  12. Simplify • Try this one

  13. PROPERTIES OF POWERS • Power of a Power: (am)n=amn • Power of a Product: (ab)m=ambm • Power of a Quotient:

  14. Properties of Powers

  15. Polynomials A monomial or a sum of monomials. Monomial – a polynomial with exactly one term Binomial – a polynomial with exactly two terms Trinomial – a polynomial with exactly three terms

  16. Polynomial Vocabulary • Term Each monomial in a polynomial • Like Terms Terms whose variable factors are exactly the same • Degree of the Polynomial The highest degree of its terms

  17. Polynomials • Indicate if the following is a polynomial, • If so classify according to the number of terms • Indicate the degree of the polynomial Not a polynomial Polynomial- Binomial- 9

  18. Polynomial Vocabulary(continued) • Leading Term The term with the highest degree • Leading Coefficient The coefficient of the leading term

  19. Descending Order • A polynomial is written in descending order for the variable x when the term with the greatest exponent for x is first, and each subsequent term has an exponent for x less than the prior term. • Example: Write the following in descending order for the variable a. 4a4 + a2 - 7a3 +6a5 + 12a8 + 4 12a8 + 6a5 + 4a4 - 7a3 + a2 + 4

  20. (2a3+5a-7) + (a3-3a+2) 3a3+2a-5 (3b3+2b2-4b+3) - (b3-2b2+3b-4) 2b3+4b2-7b+7 -3y(4y2+2y-3) -12y3 - 6y2 + 9y Simplify

  21. Multiplying Polynomials

  22. Multiplying Polynomials

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