One factor ofx^4 + x^2 +1 is

CTET 2 Math and Science Feb 2014 Paper

Question : 39 of 120

Marks: +1, -0

One factor of

x^4 + x^2 +1

Solution:

x^{4}+x^{2}+1

=x^{4}+x^{2}+x^{2}+1-x^{2}

=x^{4}+2x^{2}+1-x^{2}

=(x^{2})^{2}+2×x^{2}×1+(1)^{2}-(x)^{2}

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

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

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