Question

When the polynomial P(x) = x^3 + 3x^2 – 2Ax + 3,where A is constant, is divided by x^2 + 1 , we get a remainder equal to –5x, find A?

Answer 1

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p(x)= q(x)×g(x)+r(x)
x^3+3x^2-2Ax+3== q(x)× x^2+1-5x
x^3+3x^2-2Ax+3/x^2+1==-5x
1x-2Ax= -5x
-2Ax= -5x-1x
-2Ax=-6x
2A=6
A=3

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