IIT JEE , AIEEE Forum - Mathematics , Algebra

shinee

the remainders of the polynomial f(x) when divided by x+1, x-2 are 6,15,3 the remainder of f(x) when divided by (x+1)(x+2)(x-2) is

1)2x²-3x+1
2)3x² -2x+1
3)2x² -x-3
4)3x² -2x+1

spideyunlimited

hey plz check ur question....somethin missin or incorrect .. ?

shinee

even i thought so, i think the question is
the remainders of the polynomial f(x) when divided by x+1, x+2,x-2 are 6,15,3 the remainder of f(x) when divided by (x+1)(x+2)(x-2) is

1)2x2 -3x+1
2)3x2 -2x+1
3)2x2 -x-3
4)3x2 -2x+1

hsbhatt

The degree of the remainder when f(x) is divided by a polynomial of degree n, is at most (n-1). Here (x+1)(x+2)(x-2) is a cubic and hence the remainder will be at most a quadratic. Assume it to be ax^2+bx+c

Hence

f(-1) = 6; f(-2) = 15; f(2) = 3 (by Remainder Theorem)

So now you can set up a system of three equations in three variables and you are through.

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