Solve $16 + 8 x - x^{6} - 8 x^{3} - 2 x^{4} + x^{2}$ by $x + 4 - x^{3}$

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Solution

Let,
$f (x) =$ $16 + 8 x - 8 x^{3} - 2 x^{4}$ .
Now the remainder when $f (x)$ is divided by $x - 1$ will be $f (1)$ [ According to the remainder theorem]
Now $f (1) = 16 + 8 - 8 - 2 = 14$

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