1 / 22

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

guang
Download Presentation

Monomials

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related