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X^3 - x^2 + ax + x - a - 1

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Q. FACTORISE :

X^3 - x^2 + AX + x - a - 1

Sol.

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


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