$\frac{3 x^{4} + x^{3} + 6 x^{2} - 16 x - 6}{3 x + 1}$ = ? (Use division algorithm method).

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Solution

$x^{3} + 2 x - 6$
$3 x + 1) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 3 x^{4} + x^{3} + 6 x^{2} + 6 x - 6$
$3 x^{4} + x^{3}$
_______
$6 x^{2} - 16 x$
$6 x^{2} + 2 x$
_
$- 18 x - 6$
$- 18 x - 6$
_____
$0$

$\frac{3 x^{4} + x^{3} + 6 x^{2} - 16 x - 6}{3 x + 1} = 0$

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