Question

What should be added to the polynomial x cube minus 2x square minus 3x minus 4 so that it is completely divisible by x square minus x

Answer 1

$Let \:p(x) = x^{3}-2x^{2}-3x-4 \: and \\g(x) = x^{2}-x$

x²-x) x³-2x²-3x-4 (x-1

****** x³-x²

_____________

********* -x²-3x

********* -x²+x

________________

Remainder (-4x-4)

$p(x) \:is \: completely \: Divisible \:by \:g(x)\\</p><p>if \: the \: remainder \: should \:be\:zero$

$Remainder = 0$

$\implies -4x - 4 = 0$

$\implies (4x+4) = 0$

Therefore.,

$\red{ Required \: polynomial \: should \:be}\\\red{added \: to \: p(x) \:is } \green {= 4x+4}$

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