Let $S = \left\{ x^{3} + ax^{2} + bx + c:a,b,c \in N \right.\ $ and $a,b,c \leq$ 20 } be a set of po

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Let $S = \left\{ x^{3} + ax^{2} + bx + c:a,b,c \in N \right.\ $ and $a,b,c \leq$ 20 } be a set of polynomials. Then the number of polynomials in S , which are divisible by $x^{2} + 2$, is

Accepted Answer

$\ x^{3} + ax^{2} + bx + c = \left( x^{2} + 2 \right)\left( x + \frac{c}{2} \right)$

$$\begin{matrix} & x^{2}:a = \frac{c}{2} \\ & x:b = 2 \\ & b = 2,a = \frac{c}{2}c \in \{ 2,4,\ldots,20\} \end{matrix}$$

Number of polynomials in ' $S$ ' will be 10.

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