Question

The remainder when x^5 +kx² is divided by (x-1)(x-2) (x-3) contains no term in x² .Then find the value of k.

Answer 1

step1:- equation of standard form of (x-1)(x-2)(x-3)=x^36x^2+(1 x 2 + 2 x 3 +3 x 1)-6=x^3-6x^2+11x-6

step2:- divide both
x^3-6x^2+11x-6)x^5+kx^2(x^2+6x+25
x^5-6x^4+11x^3-6x^2
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6x^4-11x^3+(6+k)x^2
6x^4-36x^3+66x^2-36x
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25x^3+(k-60)x^2+36x
25x^3-150x^2+275x-150
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in reminder x^2 coefficient =(k-60+150)=0
k=90