Find the value of $c$ in $2 x^{3} + 4 x^{2} + c x$ if $x + 2$ is the factor.

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Solution

The correct option is A $0$
$f (x) = 2 x^{3} + 4 x^{2} + c x$
$f (- 2) = 2 \times (- 2)^{3} + 4 \times (- 2)^{2} + c \times (- 2)$
$= - 8 \times 2 + 4 \times 4 - 2 c$
$= - 16 + 16 - 2 c$
But $f (- 2) = 0$ since $(x + 2)$ is a factor of the given polynomial.
Hence, $- 2 c = 0$
$∴ c = 0$

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