1 / 12

Polynomials and Polynomial Functions

Chapter 5. Polynomials and Polynomial Functions. Chapter Sections. 5.1 – Addition and Subtraction of Polynomials 5.2 – Multiplication of Polynomials 5.3 – Division of Polynomials and Synthetic Division 5.4 – Factoring a Monomial from a Polynomial and Factoring by Grouping

dorismiles
Download Presentation

Polynomials and Polynomial Functions

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. Chapter 5 Polynomials and Polynomial Functions

  2. Chapter Sections 5.1 – Addition and Subtraction of Polynomials 5.2 – Multiplication of Polynomials 5.3 – Division of Polynomials and Synthetic Division 5.4 – Factoring a Monomial from a Polynomial and Factoring by Grouping 5.5 – Factoring Trinomials 5.6 – Special Factoring Formulas 5.7-A General Review of Factoring 5.8- Polynomial Equations

  3. Addition and Subtraction of Polynomials § 5.1

  4. Find the Degree of a Polynomial A polynomial is a finite sum of terms in which all variables have whole number exponents and no variable appears in a denominator. • 3x2 + 2x + 6 is a polynomial in one variable x • x2y – 7x + 3 is a polynomial in two variables x and y • x1/2 is not a polynomial because the variable does not have a whole number exponent

  5. Identifying Polynomials The degree of a termof a polynomial in one variable is the exponent on the variable in that term. Example: 5x6 (Sixth) 4x3 (Third) 7x (First) 9 (Zero) The degree of a polynomialis the same as that of its highest-degree term. Example: 5x6 + 4x3 – 7x + 9 (Sixth)

  6. Find the Degree of a Polynomial The leading term of a polynomial is the term of highest degree. The leading coefficient is the coefficient of the leading term. Example: 2x5 – 3x2 + 6x – 9 The degree of the polynomial is 5, the leading term is 2x5 and the leading coefficient is 2.

  7. Identifying Polynomials A polynomial is written in descendingorder (or descending powers) of the variable when the exponents on the variable decrease from left to right. Example: 5x6 + 4x3 – 7x + 9 A polynomial with one term is called a monomial. A binomialis a two-termed polynomial. A trinomialis a three-termed polynomial.

  8. Evaluate Polynomial Functions Apolynomial function is an expression used to describe the function in a polynomial. Example: For the polynomial function P(x) = 4x3 – 6x2 -2x + 9, find P(0). P(0) = 4(0)3 – 6(0)2 -2(0) + 9 = 0 – 0 – 0 + 9 = 9

  9. Understand Graphs of Polynomial Functions These graphs have a positive leading coefficient, and therefore, the function continues to increase to the right of some value of x.

  10. Understand Graphs of Polynomial Functions These graphs have a negative leading coefficient, and therefore, the function continues to decrease to the right of some value of x.

  11. Adding Polynomials To add polynomials, remove parentheses if any are present. Then combine like terms. Example:

  12. Subtracting Polynomials • Use the distributive property to remove parentheses. (This will have the effect of changing the sign of every term within the parentheses of the polynomial being subtracted.) –(4x3 + 5x2 – 8) = – 4x3– 5x2 + 8 • Combine like terms. Example: (5x – 6) – (2x – 3) = 5x – 6 – 2x + 3 = 3x – 3

More Related