How do you divide $24x^4+31^3+7x^2+4x+10$ by $3x+2$ ?

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Answer 1 · 2016-08-19T07:29:13

The Quotient Poly. is $(8x^3+5x^2-x+2)$ .

The Reminder is $6$ .

it is assumed that the Dividend Poly. is

$: p(x)=24x^4+31x^3+7x^2+4x+10$ , instead of as stated in the

Problem $: 24x^4+31^3+7x^2+4x+10$ .

We split the terms of $p(x)$ as under :

$p(x)=ul(24x^4+16x^3)+ul(15x^3+10x^2)-ul(3x^2-2x)+ul(6x+4)+6$

$=8x^3(3x+2)+5x^2(3x+2)-x(3x+2)+2(3x+2)+6$

$=(3x+2)(8x^3+5x^2-x+2)+6$

Therefore, dividing $p(x)$ by $(3x+2)$ , the Quotient Poly. is

$(8x^3+5x^2-x+2)$ and the Reminder is $6$ .

Enjoy Maths.!

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