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Popular >

factor a^6-2a^3+1

Solution

factor

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

Solution

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

Solution steps

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

Use the rational root theorem

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

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

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

Factor

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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