Factorize: $x^{2} + 3 x + 2 + a x + 2 a$

(x + a) (x + 1 + a)

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(x + 1) (x + 1 + a)

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(x + 2) (x + 1 + a)

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(x + 1) (x + 2 + a)

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Solution

The correct option is C $(x + 2) (x + 1 + a)$
$\Rightarrow x^{2} + 3 x + 2 + a x + 2 a$
$\Rightarrow [x^{2} + 3 x + 2] + [a x + 2 a]$
$\Rightarrow [x^{2} + x + 2 x + 2] + [a (x + 2)]$
$\Rightarrow [x (x + 1) + 2 (x + 1)] + [a (x + 2)]$
$\Rightarrow [(x + 1) (x + 2)] + [a (x + 2)]$
$\Rightarrow (x + 1) (x + 2) + a (x + 2)$
$\Rightarrow (x + 2) (x + 1 + a)$

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x^{2} + 3 x + 2 + a x + 2 a

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x^{2} + \frac{2}{3} x + \frac{1}{9}

Factorize : $x^{2} - 1 - 2 a - a^{2} .$

A (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 3 & 3 x & 3 x^{2} + 2 a^{2} 3 x & 3 x^{2} + 2 a^{2} & 3 x^{3} + 6 a^{2} x 3 x^{2} + 2 a^{2} & 3 x^{3} + 6 a^{2} x & 3 x^{4} + 12 a^{2} x^{2} + 2 a^{4} \end{matrix} ∣ ∣ ∣ ∣ ∣,

a \in R

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