Chapter 4 Products and Factors of Polynomials. Section 4-1 Polynomials.
Operations with Functions and Polynomials 1-3 and 1-4 Unit 1 English Casbarro.
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Transcript of Operations with Functions and Polynomials 1-3 and 1-4 Unit 1 English Casbarro.
Operations with Functions and Operations with Functions and PolynomialsPolynomials1-3 and 1-41-3 and 1-4
Unit 1Unit 1
English CasbarroEnglish Casbarro
Operations with FunctionsYou really already know how to do this. Recall, Combining Like Terms.Ex. 4x4 - 5x2 + 6 – 7x4+ 10x2 -13.
You would combine: 4x4 -7x4 - 5x2 + 10x2 + 6 -13 = -3x4 + 5x2 - 7
Graphic Organizer-Function Notation
Fill in the following table.
Operation Notation
Addition
Subtraction
Multiplication
Division
Warm-up: Function NotationGiven f(x) = 2x2 – 8 , g(x) = x2 + 5x + 6,
and h(x) = 2x + 4, find each function and define the domain.
1. (f + g)(x) 2. (f – g)(x)
3. (g + h)(x) 4. (g – h)(x)
5. f(x) + h(x) 6. (fh)(x)
7. 8. )()(
xgxf
)()(
xfxh
1-4: PolynomialsDefinitionsA monomial is a number, a variable, or a product of both
A polynomial is a monomial or a sum or difference of monomials.
Each monomial in a polynomial is a term.
The degree of a monomial is the sum of the exponents of the variables.
The degree of a polynomial is the highest degree of all of the terms of the polynomial.
The leading coefficient is the coefficient of the term with the highest degree.
A polynomial function is a function whose rule is a polynomial.
Identifying Polynomials:
Identifying Polynomials
Polynomials: 3x 4 2z 12 + 9z 3 ½a 7 0.15x 101 3t 2 – t 3
Not Polynomials: 3x |2b3 – 6b| m0.75 – m 25
8y x
21
Ex. 1 Identifying the degree of a MonomialIdentify the degree of each monomial.
A. x4 B. 12
C. 4a2b D. x 3y 4z
You Try:Identify the degree of each monomial.
1a. x 3 1b. 7 1c. 5x 3y 2 1d. a 6bc 2
Standard Form of a Polynomial
Classifying by number of terms and by degrees.
Name Terms Example
Monomial 1 7, x5, 3x
Binomial 2 x5 - 7x
Trinomial 3 x2 + 2x + 3
Turn in the following problems:1. Business The manager of a gift-basket business will ship the baskets anywhere in the country. The cost to mail a basket based on its weight, x, in pounds is given by C(x) = 0.03x 3 – 0.75x 2 + 4.5x + 7. a. What is the cost of shipping a 7-pound gift basket? b. What is the cost of shipping a 19-pound gift basket?
2. Reasoning The total number of lights in a triangular lighting rig is related to the triangular numbers, as shown below. The nth triangular number is given by .
a. Write a polynomial function that represents the (n + 1)th triangular number, T(n + 1). b. The difference between two consecutive triangular numbers is T(n + 1) – T(n). Subtract these two polynomial functions and state a conclusion about the difference between consecutive triangular numbers.
nnnT21
21
)( 2