Factorize the following expression:
$x^{3} - x^{2} + a x + x - a - 1$

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Solution

Factorizing the given expression:
$x^{3} - x^{2} + a x + x - a - 1 = x^{3} - x^{2} + a x - a + x - 1 (R e a r r a n g i n g t h e t e r m s) = x^{2} (x - 1) + a (x - 1) + (x - 1) = (x - 1) (x^{2} + a + 1) (T a k i n g x - 1 c o m m o n)$
Hence, after factorizing we get $x^{3} - x^{2} + a x + x - a - 1 = (x - 1) (x^{2} + a + 1) .$

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Factorize the following expression:x3-x2+ax+x-a-1

Factorizing the given expression:x3-x2+ax+x-a-1=x3-x2+ax-a+x-1(Rearrangingtheterms)=x2(x-1)+a(x-1)+(x-1)=(x-1)(x2+a+1)(Takingx-1common)Hence, after factorizing we get x3-x2+ax+x-a-1=(x-1)(x2+a+1).

Factorize the following expression:
$x^{3} - x^{2} + a x + x - a - 1$