Answer :

Formula used.

If f(x) is a polynomial with degree n

Then (x – a) is a factor of f(x) if f(a) = 0

1^{st} we find out zero of polynomial x + 1

x + 1 = 0

x = – 1

if f(x) is x^{4} + x^{2} + x + 1

then putting x = – 1;

f( – 1) = ( – 1)^{4} + ( – 1)^{2} + ( – 1) + 1

= 1 + 1 – 1 + 1

= 2

Conclusion.

∴ (x + 1) is not a factor of x^{4} + x^{2} + x + 1

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