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

Aug 19, 2016

The Quotient Poly. is $\left(8 {x}^{3} + 5 {x}^{2} - x + 2\right)$.

The Reminder is $6$.

Explanation:

it is assumed that the Dividend Poly. is

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

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

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

$p \left(x\right) = \underline{24 {x}^{4} + 16 {x}^{3}} + \underline{15 {x}^{3} + 10 {x}^{2}} - \underline{3 {x}^{2} - 2 x} + \underline{6 x + 4} + 6$

$= 8 {x}^{3} \left(3 x + 2\right) + 5 {x}^{2} \left(3 x + 2\right) - x \left(3 x + 2\right) + 2 \left(3 x + 2\right) + 6$

$= \left(3 x + 2\right) \left(8 {x}^{3} + 5 {x}^{2} - x + 2\right) + 6$

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

$\left(8 {x}^{3} + 5 {x}^{2} - x + 2\right)$ and the Reminder is $6$.

Enjoy Maths.!