What is factor x^{10}-1 ?

The solution to factor x^{10}-1 is (x+1)(x^4-x^3+x^2-x+1)(x-1)(x^4+x^3+x^2+x+1)

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factor x^{10}-1

factor

x^{10} - 1

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

Solution steps

x^{10} - 1

Apply exponent rules

= (x^{5})^{2} - 1^{2}

Apply Difference of Two Squares Formula:

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

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

= (x^{5} + 1) (x^{5} - 1)

Factor

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

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

Factor

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

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

(\frac{- 8 x ^{4} y ^{- 2}}{3 z ^{2}})^{- 1}

- 4 (x - 1) \leq 40

x^{21}

\frac{2}{4} - \frac{1}{5}

x < - 1 and x < 1

What is factor x^{10}-1 ?
The solution to factor x^{10}-1 is (x+1)(x^4-x^3+x^2-x+1)(x-1)(x^4+x^3+x^2+x+1)