# Factor And Remainder Theorem Pdf

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*Today's lesson aims to provide practice doing long division, interpreting the results of long division, using synthetic substitution, and "discovering" the remainder theorem. For the bulk of the class, students will be working on a series of problems designed to accomplish these goals. I will be circulating among the students offering assistance to groups and individuals as needed.*

- Polynomial remainder theorem
- 2. The Remainder Theorem and the Factor Theorem
- Factor Theorem
- 2. The Remainder Theorem and the Factor Theorem

*So to find the remainder after dividing by x-c we don't need to do any division:.*

The most valuable use of this discovery is to determine if the divisor x - a is a factor of the dividend. If x - a is a factor of f x , the remainder will be zero. You can quickly make this determination by plugging a into f x to see if the result is zero. This special use of the Remainder Theorem to determine a factor is call the Factor Theorem :.

## Polynomial remainder theorem

The polynomial remainder theorem follows from the theorem of Euclidean division , which, given two polynomials f x the dividend and g x the divisor , asserts the existence and the uniqueness of a quotient Q x and a remainder R x such that. Although polynomial long division is more difficult than evaluating the function itself, synthetic division is computationally easier. Thus, the function may be more "cheaply" evaluated using synthetic division and the polynomial remainder theorem. The factor theorem is another application of the remainder theorem: if the remainder is zero, then the linear divisor is a factor. Repeated application of the factor theorem may be used to factorize the polynomial. From Wikipedia, the free encyclopedia.

Interpret the remainder of a polynomial divided by x-k. Given one factor of a polynomial function, use division to fin the remaining factors. We are taking a new approach to dividing polynomials with this lesson. We start with the area box method to demonstrate how to multiply two polynomials using the box. The students should notice how to find the like terms from the box and combine them to answer the question.

## 2. The Remainder Theorem and the Factor Theorem

In this section we learn about the factor and remainder theorems. These theorems are at the heart of factoring polynomials and finding a polynomial's roots or zeros. We state each theorem as well as see how they can be used with tutorials. We also work through some exam type questions , which can be downloaded as pdf worksheets. In this tutorial , we learn how to use the remainder theorem to find the remainder obtained when dividing a polynomial by a linear. In doing so, we also see how to actually divide a polynomial by a linear using Horner's Method for evaluating polynomials.

Section 4 The factor theorem and roots of polynomials The remainder theorem told us that if p x is divided by x a then the remainder is p a. Go back to 'Polynomials' Book a Free Class. Teacher can use this while teaching the section. Factor theorem is usually used to factor and find the roots of polynomials. Siyavula's open Mathematics Grade 12 textbook, chapter 5 on Polynomials covering Factor theorem Remainder theorem and factor theorem worksheets. Understand the Factor Theorem, that a is a root of a polynomial function if and only if x-a is a factor of the function. Example 1 shows how to divide polynomials using a method called.

Solving and simplifying polynomials Thus, from arithmetic, we know that we can express a In our study of quadratics, one of the methods used to dividend as: simplify and solve was factorisation. Examine the following division problems in algebra A more general name for a quadratic is a polynomial and note the similarities. The method of factorisation worked for Division of a polynomial by a linear expression quadratics whose solutions are integers or rational We can apply the same principles in arithmetic to numbers. The dividend is divided by the divisor. The result is the quotient and the remainder is what is left over.

and factor theorems to find factors of polynomials. A Generally when a polynomial is divided by a linear expression there is a remainder. 5) 3)(2() 4. 3.

## Factor Theorem

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### 2. The Remainder Theorem and the Factor Theorem

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Chapter 3. Section Factor Theorem and Remainder Theorem. In the last section, we limited ourselves to finding the intercepts, or zeros, of polynomials.

4 comments

Remainder and Factor Theorem Find the remainder using the remainder theorem and.

The polynomial p is called the dividend; d is the divisor; q is the quotient; r is the remainder. If r(x) = 0 then d is called a factor of p. The proof of Theorem is.

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