What is factor x^9-x^6-x^3+1 ?

The solution to factor x^9-x^6-x^3+1 is (x-1)^2(x+1)(x^2+x+1)^2(x^2-x+1)

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factor x^9-x^6-x^3+1

factor

x^{9} - x^{6} - x^{3} + 1

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

Solution steps

x^{9} - x^{6} - x^{3} + 1

= (x^{9} - x^{6}) + (- x^{3} + 1)

Factor out

x^{6}

from

x^{9} - x^{6} : x^{6} (x^{3} - 1)

Factor out

- 1

from

- x^{3} + 1 : - (x^{3} - 1)

= x^{6} (x^{3} - 1) - (x^{3} - 1)

Factor out common term

(x^{3} - 1) : (x^{3} - 1) (x^{6} - 1)

= (x^{3} - 1) (x^{6} - 1)

Factor

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

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

Factor

x^{6} - 1 : (x + 1) (x - 1) (x^{2} + 1 + x) (x^{2} + 1 - x)

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

Apply exponent rule:

aa = a^{2}

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

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

Simplify

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

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

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

1 = \frac{1}{5} (x - 25)

5 (2 x + 1) = 6 x + 13

e^{2} x - 9 e x + 20 = 0

- \frac{\frac{16}{21}}{( - \frac{8}{3} )}

- (\frac{1}{3})^{0}

What is factor x^9-x^6-x^3+1 ?
The solution to factor x^9-x^6-x^3+1 is (x-1)^2(x+1)(x^2+x+1)^2(x^2-x+1)