Download presentation
Presentation is loading. Please wait.
Published byRosalyn Terry Modified over 8 years ago
1
Monomials An expression that is either a number, a variable, or a product of numerals and variables with whole number exponents.
2
Monomials 5x 3 y 12 is a monomial is not a monomial
3
Vocabulary Constants monomials that contain no variables Example3or-22 Coefficient Numeric factor of the term -32x 3 y 12 z 15 coefficient = -32
4
Vocabulary (continued) Degree of a Monomial The sum of the exponents of the variables 3x 4 degree = 4 -32x 3 y 12 z 15 degree = 3+12+15 = 30 5degree = 0
5
Vocabulary (continued) Power An expression in the form of x n Can also refer to the exponent
6
Product of Powers For any real number a and integers m and n, a m · a n =a m+n 2 3 · 2 5 =2 · 2 · 2 · 2 · 2 · 2 · 2 · 2= 2 8
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 (-2a 3 b)(-5ab 4 ) Multiply Coefficients (-2)(-5)=10 Multiply Variables (a 3 )(a) = a 4 (b)(b 4 ) = b 5 10a 4 b 5
12
Simplify Try this one
13
PROPERTIES OF POWERS Power of a Power: (a m ) n =a mn Power of a Product: (ab) m =a m b m 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. 4a 4 + a 2 - 7a 3 +6a 5 + 12a 8 + 4 12a 8 + 6a 5 + 4a 4 - 7a 3 + a 2 + 4
20
Simplify (2a 3 +5a-7) + (a 3 -3a+2) 3a 3 +2a-5 (3b 3 +2b 2 -4b+3) - (b 3 -2b 2 +3b-4) 2b 3 +4b 2 -7b+7 -3y(4y 2 +2y-3) -12y 3 - 6y 2 + 9y
21
Multiplying Polynomials
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.