Question

plz solve it fast .....

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Answer 1

$Given \:p(x) = -x^{3}+3x^{2}-3x+5$

$and \: g(x)=(x-1)$

x-1| -x³+3x²-3x+5|-x²+2x-1

**** -x³+x²

_____________

******** 2x²-3x+5

******** 2x²-2x

_____________

************** -x+5

************** -x+1

______________

*****************(4)

Dividend p(x) = -x³+3x²-3x+5

Divisor g(x) = x - 1

Quotient q(x) = -x²+2x-1

Remainder r(x) = 4

/* By Remainder Theorem */

p(x) = g(x) × q(x) + r(x)

Verification:

g(x) × q(x) + r(x)

(x-1)( -x²+2x-1) + 4

= x( -x²+2x-1)-1(-x²+2x-1) + 4

= -x³+2x²-x +x²-2x+1+4

= -x³+3x²-3x+5

= p(x)

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