State and prove the factor theorem

2020-02-27 20:19 Factor Theorem. Let f (x) be a polynomial. If a polynomial f (x) is divided by x c, then the remainder will be zero. That is, x c is zero or root of a polynomial f (x), which also makes (x c) is a factor of f (x). Thus, the theorem states that if f (c)0, then (xc) is a factor of the polynomial f (x).

Video transcript. This is the proof of the polynomial remainder theorem. Any function, if when you divide it by x minus a you get the quotient q of x and the remainder r, it can then be written in this way. If it's written in this way and you evaluated at f of a and you put the a over here, you're going to see that f of a state and prove the factor theorem

Mar 13, 2014 Factor Theorem. We can now state the factor theorem. The factor theorem states the following: A polynomial f(x) has a factor (x h) if and only if f(h) 0. This theorem is biconditional, which means that each condition is an effect of the other: If a polynomial f(x) has a factor of (x h), then f(h) 0.

proof of factor theorem using division Lemma (cf. factor theorem). Let R be a commutative ring with identity and let p ( x ) R [ x be a polynomial with coefficients in R. state and prove the factor theorem

The Remainder Theorem. Then the Theorem talks about dividing that polynomial by some linear factor x a, where a is just some number. Then, as a result of the long polynomial division, you end up with some polynomial answer q ( x) (the q standing for the quotient polynomial ) and In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f ( x ) \displaystyle f(x) has a factor ( x k ) \displaystyle (xk) if and only if f ( k ) An inductive proof of the Factor Theorem. Proof: Suppose deg. Then and. Clearly and is a polynomial (of degree 0). Suppose for all polynomials of degree less than or equal to, that a root implies a factor. Let be a polynomial of degree and assume a root. Now Now each for is a polynomial of degree less than or equal to, with a root, state and prove the factor theorem In this page given definition and proof for Remainder Theorem and Factor Theorem and also provided application of remainder theorem and factor theorem. Statement of Remainder Theorem: Let f(x) be any polynomial of degree greater than or equal to one and let a be any number. If f(x) is divided by the linear polynomial (xa) then the remainder is f(a). Video transcript. The polynomial remainder theorem, the polynomial remainder theorem tells us that if we take some polynomial, p of x and we were to divide it by some x minus a then the remainder is just going to be equal to our polynomial evaluated at our polynomial evaluated at a. So let's just see what's a in this case. Well in this case our a is positive three.

Video State and prove the factor theorem

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