What is factor x^6-9x^3+8 ?

The solution to factor x^6-9x^3+8 is (x-1)(x^2+x+1)(x-2)(x^2+2x+4)

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factor x^6-9x^3+8

factor

x^{6} - 9 x^{3} + 8

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

Solution steps

x^{6} - 9 x^{3} + 8

Use the rational root theorem

= (x - 1) \frac{x ^{6} - 9 x ^{3} + 8}{x - 1}

\frac{x ^{6} - 9 x ^{3} + 8}{x - 1} = x^{5} + x^{4} + x^{3} - 8 x^{2} - 8 x - 8

= (x - 1) (x^{5} + x^{4} + x^{3} - 8 x^{2} - 8 x - 8)

Factor

x^{5} + x^{4} + x^{3} - 8 x^{2} - 8 x - 8 : (x^{2} + x + 1) (x - 2) (x^{2} + 2 x + 2^{2})

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

2^{2} = 4

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

\frac{2 x + x ^{2}}{x ^{2} + 5 x + 6}

\frac{5 x ^{2} - 15 x}{x ^{2} + 2 x - 15}

(2 x - 3) (3 x + 1)

- 2 x^{2} - 32 x - 30

2 + 4 + 8 + 16 + 32 + 2^{n}

What is factor x^6-9x^3+8 ?
The solution to factor x^6-9x^3+8 is (x-1)(x^2+x+1)(x-2)(x^2+2x+4)