Question

Divide -x^3+3x^2-3x+5 by x-1-x^2 and verify the division algorithm

Answer 1

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Answer 2

$Let \: p(x) = -x^{3}+3x^{2}-3x+5 \: by \\g(x) = -x^{2}+x-1$

-x²+x-1)-x³+3x²-3x+5(x-2

********* -x³+x²-x

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************* 2x² - 2x + 5

************* 2x² -2x + 2

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*******Remainder ( 3)

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Dividend = - x³ + 3x² - 3x + 5 ,

Divisor = -x² + x - 1,

Quotient = x - 2 ,

Remainder = 3

By Division Algorithm

$\pink { Divisor \times quotient + Remainder}\\\pink {= Dividend }$

Verification:

Divisor × quotient + Remainder

= (-x² + x - 1)(x-2) + 3

= (-x² + x - 1)x + (-x² + x - 1)(-2) + 3

= -x³ + x² - x + 2x² - 2x + 2 + 3

= -x³ + 3x² - 3x + 5

= Dividend

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