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Popular >

factor x^6-2x^3+1

Solution

factor

x^{6} - 2 x^{3} + 1

Solution

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

Solution steps

x^{6} - 2 x^{3} + 1

Use the rational root theorem

= (x - 1) \frac{x ^{6} - 2 x ^{3} + 1}{x - 1}

\frac{x ^{6} - 2 x ^{3} + 1}{x - 1} = x^{5} + x^{4} + x^{3} - x^{2} - x - 1

= (x - 1) (x^{5} + x^{4} + x^{3} - x^{2} - x - 1)

Factor

x^{5} + x^{4} + x^{3} - x^{2} - x - 1 : (x^{2} + x + 1) (x - 1) (x^{2} + x + 1)

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

Simplify

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

Popular Examples

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Frequently Asked Questions (FAQ)

What is factor x^6-2x^3+1 ?
The solution to factor x^6-2x^3+1 is (x-1)^2(x^2+x+1)^2