remainder and factor theorem pdf Wednesday, April 28, 2021 12:50:41 PM

Remainder And Factor Theorem Pdf

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As we discussed in the previous section Polynomial Functions and Equations , a polynomial function is of the form:. We could write this as:.

Recall that for long division for integers, the dividing process stops when the remainder is less than the divisor. The process is similar for division of polynomials. The dividing stops when the remainder is less that the degree of the divisor.

Full Coverage: IGCSE FM Factor Theorem and Remainder Theorem

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2. The Remainder Theorem and the Factor 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.

Like in this example using Polynomial Long Division :. So to find the remainder after dividing by x-c we don't need to do any division:. We see this when dividing whole numbers. So 20 must be a factor of The curve crosses the x-axis at three points, and one of them might be at 2. We can check easily:. Hide Ads About Ads.

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 :. The factor theorem links factors and roots zeros of a polynomial. Let's take a look at some example questions:. When working with Synthetic Division , we saw a series of division problems involving a divisor of the form x - a , where the degree of the divisor was one.

2. The Remainder Theorem and the Factor Theorem

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.

Despite all of the factoring techniques we learned in Intermediate Algebra, this equation foils us at every turn. Even though we could use the 'Zero' command to find decimal approximations for these, we seek a method to find the remaining zeros exactly. The answer comes from our old friend, polynomial division. The point of this section is to generalize the technique applied here. First up is a friendly reminder of what we can expect when we divide polynomials.

11.Remainder and Factor Theorem.pdf

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Dividing Polynomials

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Presentation on Remainder and Factor Theorem

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