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Standard IX

Mathematics

Factor Theorem

let p (x) be ...

Question

let p (x) be any polynomial of degree n> 1 and let 'a' be any real number, then (x-a) is a factor of p (x), if: a)p(x)=0;b)p(a)is not equal to 0;c)p(a)=0;d)p(x)is not equal to 0

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Solution

$Let p (x) be the polynomial . Now, (x - a) is a factor of p (x) So, by factor theorem, p (a) = 0$

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let p (x) be any polynomial of degree n> 1 and let 'a' be any real number, then (x-a) is a factor of p (x), if: a)p(x)=0;b)p(a)is not equal to 0;c)p(a)=0;d)p(x)is not equal to 0

Let px be the polynomial.Now, x-a is a factor of pxSo, by factor theorem, pa = 0

$Let p (x) be the polynomial . Now, (x - a) is a factor of p (x) So, by factor theorem, p (a) = 0$