1 / 6

ACC Module #3 Unit 3.4

ACC Module #3 Unit 3.4

pwkellysr
Download Presentation

ACC Module #3 Unit 3.4

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. DemingEarly College High SchoolUnit 3.0 Advanced Algebra and Functions (AAF) 3.4 Polynomial Equations

  2. Unit 3.0 Advanced Algebra and Functions (AAF)3.4 Polynomial Equations An expression in the form of , where n is a non-negative integer, is called a monomial because it contains one unknown term. A sum of monomials is called a polynomial. For example, is a polynomial, while is a monomial. A function equal to a polynomial is called a polynomial function. The monomials in a polynomial are also called the terms of the polynomial. The constant that precede the variables are called coefficients. The highest value of the exponent of x in a polynomial is called the degree of the polynomial. So, has a degree of 3, while has a degree of 7, and has a degree of 5.

  3. Unit 3.0 Advanced Algebra and Functions (AAF)3.4 Polynomial Equations To add polynomials, add the coefficients of like powers of x. For example: Likewise, subtraction of polynomials is performed by subtracting coefficients of like powers of x. So:

  4. Unit 3.0 Advanced Algebra and Functions (AAF)3.4 Polynomial Equations To multiply two polynomials, the degree of the result will be the sum of the degrees of the two polynomials being multiplied. Also multiply each term of the first polynomial by each term of the second polynomial a add the results. For example: In the case where each polynomial has two terms, like in this example, it is helpful to remember this as multiplying the First terms, then the Outer terms, then the Inner terms, and finally the Last terms, using the mnemonic FOIL.

  5. Unit 3.0 Advanced Algebra and Functions (AAF)3.4 Polynomial Equations For longer polynomials, the multiplication process is the same, but there will be, of course more terms and there is no common mnemonic to remember each combination. The process of factoring a polynomial means to write the polynomial as a product of other (generally simpler) polynomials. Here is an example: . If a certain monomial divides every term of the polynomial, factor it out of each term, for example: [1] [2] or

  6. Unit 3.0 Advanced Algebra and Functions (AAF)3.4 Polynomial Equations [3] [4] [5] [6] It can sometimes be necessary to rewrite the polynomial in some clever way before applying the above rules. Consider the problem of factoring This does not like any of the cases for which there are rules. However, it is possible to think of this polynomial as . Now apply the third rule in the above list to simplify this: .

More Related