What is factor z^{10}-5z^5-6 ?

The solution to factor z^{10}-5z^5-6 is (z+1)(z^4-z^3+z^2-z+1)(z^5-6)

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factor z^{10}-5z^5-6

factor

z^{10} - 5 z^{5} - 6

(z + 1) (z^{4} - z^{3} + z^{2} - z + 1) (z^{5} - 6)

Solution steps

z^{10} - 5 z^{5} - 6

Use the rational root theorem

= (z + 1) \frac{z ^{10} - 5 z ^{5} - 6}{z + 1}

\frac{z ^{10} - 5 z ^{5} - 6}{z + 1} = z^{9} - z^{8} + z^{7} - z^{6} + z^{5} - 6 z^{4} + 6 z^{3} - 6 z^{2} + 6 z - 6

= (z + 1) (z^{9} - z^{8} + z^{7} - z^{6} + z^{5} - 6 z^{4} + 6 z^{3} - 6 z^{2} + 6 z - 6)

Factor

z^{9} - z^{8} + z^{7} - z^{6} + z^{5} - 6 z^{4} + 6 z^{3} - 6 z^{2} + 6 z - 6 : (z^{4} - z^{3} + z^{2} - z + 1) (z^{5} - 6)

= (z + 1) (z^{4} - z^{3} + z^{2} - z + 1) (z^{5} - 6)

a^{2 x + 6} - b^{6 y}

\frac{- x + 2}{4 - x ^{2}}

3 x + (- 4)

12 x^{2 + 11 x + 2}

What is factor z^{10}-5z^5-6 ?
The solution to factor z^{10}-5z^5-6 is (z+1)(z^4-z^3+z^2-z+1)(z^5-6)