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If one of the factor of x4 + x2 + 1 is (x2 + x + 1) then what is the other factor?
  • a)
    x2 - x + 1
  • b)
    x2 + x - 1
  • c)
    x2 + x + 1
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
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If one of the factor of x4 + x2 + 1 is (x2 + x + 1) then what is the o...
Explanation:

Given: x^4 + x^2 + 1 and one factor is x^2 + x + 1
To find the other factor, we can use polynomial division or factor theorem.

Using Polynomial Division:
- Perform polynomial division of x^4 + x^2 + 1 by x^2 + x + 1.
- The quotient will be x^2 - x + 1.
Therefore, the other factor is x^2 - x + 1.

Alternatively, Using Factor Theorem:
- Since x^2 + x + 1 is a factor of x^4 + x^2 + 1, it means that when x^2 + x + 1 is divided into x^4 + x^2 + 1, the remainder is zero.
- We can set x^2 + x + 1 equal to zero and solve for x to find the roots.
- The roots are complex, which means the conjugate factor is x^2 - x + 1.
Hence, the other factor is x^2 - x + 1.
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