Find the remainder using remainder theorem, when:
$8 x^{4} + 12 x^{3} - 2 x^{2} - 18 x + 14$ is divided by $x + 1$

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Solution

According to remainder theorem when $f (x)$ is divided by $(x + 1)$ , Remainder $= f (- 1)$
$f (x) = 8 x^{4} + 12 x^{3} - 2 x^{2} - 18 x + 14$
$f (- 1) = 8 (- 1)^{4} + 12 (- 1)^{3} - 2 (- 1)^{2} - 18 (- 1) + 14$
$= 8 - 12 - 2 + 18 + 14 = 26$
$∴$ Remainder $= 26$

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