InterviewSolution
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InterviewSolution
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x**6 %2B 5*x**3 %2B 8 |
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Answer» x^6 + 5x^3 + 8 = (x)^6+ 5x^3 + 8 + x^3 - x^3 = x^6 + 6x^3 + 8 - x^3 [By adding and subtracting x^3 on both sides] = (x^2)^3+ (2)^3+ (-x)^3 - 3 × (x^2) × (2) × (-x) According to the identity, x^3 + y^3 + z^3 - 3xyz = (x + y + z) (x^2 + y^2 + z^2 – xy – yz – zx) = (x^2 + 2 - x)[(x^2)^2 + (2)^2 + (-x)^2 - (x^2) × (2) - (2) × (-x) - (x^2) × (-x)) = (x^2 - x + 2)(x^4 + x^2 + 4 - 2x^2 + 2x + x^3) = (x2 - x + 2)(x4 + x3 - x2 + 2x + 4) Thus, the facotrs of x6 + 5x3 + 8 are (x2 - x + 2)(x4 + x3 - x2 + 2x + 4). |
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