$4 x^{3} + x^{2} + 5 x + 8$ = $(x + 1)$ $\times$ .

(4 x^{2} - 3 x + 8)

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(x^{2} + 8 x - 3)

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(x^{2} - 3 x + 8)

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(4 x^{2} + 3 x - 8)

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Solution

The correct option is A $(4 x^{2} - 3 x + 8)$
The quotient obtained when ( $4 x^{3} + x^{2} + 5 x + 8$ ) is divided by ( $x + 1$ ) is the other factor.

$\begin{matrix} 4 x^{2} - 3 x + 8 x + 1 4 x^{3} + x^{2} + 5 x + 8 4 x^{3} + 4 x^{2} - --------- - - 3 x^{2} + 5 x - 3 x^{2} - 3 x - ---------- - 8 x + 8 8 x + 8 - ----- - 0 \end{matrix}$

Hence, the other factor is $4 x^{2} - 3 x + 8$ .

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