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`        A certain polynomial P(x), x€R when divided by x-a, x-b, x-c leaves remainders a,bb,c respectively. then find the remainder when P(x) is divided by (x-a)(x-b)(x-c) where a,b,c are distinct.`
3 years ago Harsh Patodia
IIT Roorkee
906 Points
```							Using Remiander theoremf(a) is the remainder when f(x) is divided by x-awhen f(x) is divided by q(x) the remainder will be having degree less than q(x) so when P(x) is divided by (x-a),(x-b),(x-c) the remainders are P(a),P(b) and P(c) respectivelytherefore P(x)=(x-a)(x-b)(x-c)g(x) + (px^2+qx+r) where (px^2+qx+r)is remainder g(x) is the quotientP(a)=pa^2+qa+r=a --- (I)P(b)=pb^2+qb+r=b----(II)P(c)=pc^2+qc+r=c-----(III)Closely observing u can q=1 p and r =0So remiander will be xand Secondly you could have also solved equations by using II-I and III-I.
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3 years ago
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