Thread: polynomial division

please help to solve following problem-

If a polynomial p(x) of degree more then 2 is divided by (x-2), the remainder is one(1) & if divided by (x-3), remainder is three(3), what will be the remainder if it is divided by (x-2) (x-3).

Thanks

Originally Posted by raj01b

please help to solve following problem-

If a polynomial p(x) of degree more then 2 is divided by (x-2), the remainder is one(1) & if divided by (x-3), remainder is three(3), what will be the remainder if it is divided by (x-2) (x-3).

Thanks

HI

p(x)=q(x)(x-2)(x-3)+Ax+B

where q(x) here is the quotient and Ax+B , the remainder .

p(2)=1 , p(3)=3

p(2)=2A+B=1 --- 1

p(3)=3A+B=3 ----2

Solve the simultaneous equations .

Hi Mr Mathaddict,
Thank you very much for your help.