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Polynomials & Rational Functions

Review question

Can we show $(x^2+1)(x+1)=(a^2+1)(a+1)$ has just one real root?
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Ref: R9108

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Suggestion

Prove that, if \(a\) is real, the equation \[(x^2+1)(x+1)=(a^2+1)(a+1)\] has one and only one real root.

Can we identify one obvious root of this equation?

Could we then factorise to find any other possible roots?