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# long division to find the quotient

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use long division to find the quotient A(x) and the remainder R(x) is divided by d(x) and express P(x) in the form d(x) times Q(x) + R(x). P(x)=x^3+1x^2-3X+85 D(x)=x+5

Guest Mar 5, 2017
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I have changed you question so that it makes sense.

use long division to find the quotient A(x) and the remainder  R(x) when P(x) is divided by d(x) and express P(x) in the form d(x) times Q(x) + R(x).

P(x)=x^3+1x^2-3X+85         D(x)=x+5

P(-5)=-125+25+15+85=0   therefore this is not going to be a remainder   :)

$$\begin{array}{rrrrrrrr}\\ &x^2&-4x&+17\\\hline x+5|&x^3&+1x^2&-3x&+85\\ &x^3&+5x^2\\\hline &&-4x^2&-3x&+85\\ &&-4x^2&-20x\\\hline &&&17x&+85\\ &&&17x&+85\\\hline &&&&0 \end{array}$$

$$P(x)=d(x)Q(x)+R(x)\\ where\\ P(x)=x^3+1x^2-3X+85\\ Q(x)=(x^2-4x+17)\\ D(x)=x+5\\ R(x)=0$$

Melody  Mar 5, 2017
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Thank you!

Guest Mar 5, 2017