When 2 is subtracted from $p (x)$ , we get a polynomial whose factors are $(x + 2)$ and $(x + 3)$ . What is $p (x)$ ?

x^{2} + 5 x + 8

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x^{2} + 5 x + 6

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x^{3} + 5 x + 8

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5 x + 8

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Solution

The correct option is A $x^{2} + 5 x + 8$
Given,
$p (x) - 2 = (x + 2) (x + 3)$

We know,
$(x + a) (x + b) = x^{2} + (a + b) x + a b$
$∴$
$(x + 2) (x + 3)$ = $x^{2} + (2 + 3) x + (2) (3)$
$\Rightarrow$ $x^{2} + 5 x + 6$

$∴$
$p (x) - 2 = x^{2} + 5 x + 6$
$\Rightarrow$ $p (x) = x^{2} + 5 x + 8$

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