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Factorize the polynomial in $$x$$ given by $$(t^2+1)x^3 - (t^2-1)x^2 - (t^2+1)x + (t^2-1)$$
Correct Answer: 0
Group the terms in pairs as $$(t^2+1)x(x^2 - 1) - (t^2-1)(x^2 - 1)$$. Taking out the common factor gives $$(x^2 - 1)\left[(t^2+1)x - (t^2-1)\right]$$. Hence the polynomial factorizes as $$(x - 1)(x + 1)\left[(t^2+1)x - t^2 + 1\right]$$.
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