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Factorize the equation $x^{2} + 3 x - (a^{2} + a - 2)$ .

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

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

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

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

answer is B.

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Detailed Solution

x^{2} + 3 x - (a^{2} + a - 2) = x^{2} + 3 x - (a - 1) (a + 2)

= x^{2} + [(a + 2) - (a - 1)] x - (a - 1) (a + 2)

= [x + (a + 2)] [x - (a - 1)] = (x + a + 2) (x - a + 1)

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