Question

if x³+5x²+10k leaves remainder -2x +10 when dividend by x²+2,then k =??​

Answer 1

Answer:

x^3+5x^2–10k/(x^2+2)=-2x/(x^2+2)+m where m is a multiple of (x^2+2)

Simplify by multiplying with (x^2+2) you get

x^3+5x^2–10k=(x^2+2)m-2x

Looking at x^3 and x^2 only m must contain an x and 5 to get x^3 and 5x^2

let m=(x+5), you get

x^3+5X^2–10k= (x^2+2)(x+5)-2x

RHS upon expansion gives : x^3+5x^2+10

therefore -10k=10 and k=-1

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