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What is remainder theorem? With proof.

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What is remainder theorem? With proof.

Posted by Ashleesha Gupta 7 years, 6 months ago

CBSE > Class 09 > Mathematics

1 answers

Ashleesha Gupta 7 years, 6 months ago

Let p(x) be any polynomial whose degree is greater than or equal to one and a be any real number. If p(x) is divided by (x - a), then the remainder is equal to p(a). Proof: Let q(x) be the quotient and r(x) be the remainder when p(x) is divided by (x - a). Then, Let p(x) = (x - a) q(x) + r(x) ........1 Where r(x)=0. But, (x - a) is polynomial of degree 1 and a polynomial of degree less than 1 is a constant. Therefore, either r(x) =0 or r(x) = constant. Let r(x) =r.then, P(x) =(x - a) q(x) + r. ......2 Putting x=a in 2 we get P(a) =(a - a) q(a) +r => p(a) = 0 * q(a)+r => p(a) =0+r => p(a) = r This shows that the remainder is p(a) when p(x) is divided by (x - a).

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