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(x + a)(x +b)= x^2 + x(a+ b) + ab

Px=x3+x2+x+1,...

Question

$P (x) = x^{3} + x^{2} + x + 1$ , one fator is $(x + 1)$ , other is _________.

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Solution

$P (x) = x^{3} + x^{2} + x + 1$

$= x^{3} + x + x^{2} + 1$

$= x (x^{2} + 1) + 1 (x^{2} + 1)$

$= (x^{2} + 1) (x + 1)$

$∴$ Othere factor is $(x^{2} + 1)$

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