One factor of x^{4} + x² + 1 is

Correct Answer is : x2−x+1x² }- x + 1x2−x+1

Correct Answer is : x2−x+1x² }- x + 1x2−x+1

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CTET Paper II (Mathematics and Science) Feb 2014 Solved Paper

Question : 39 of 150

Marks: +1, -0

One factor of x^{4} + x^{2} + 1 is

Solution:

Concept:

We use the identity

a^2 - b^2 = (a+b)(a-b)

after rearranging the given expression as a perfect square minus another square.

Explanation:

Start with

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

Add and subtract

x^{2}

to complete a square:

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

The first three terms form

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

, giving

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

Now apply the difference of squares:

[(x^{2}+1) - x] \, [(x^{2}+1) + x]

This simplifies to

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

Thus, one factor is

x^{2} - x + 1

Answer:

Option C:

x^{2} - x + 1

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