What is factor x^7-128 ?

The solution to factor x^7-128 is (x-2)(x^6+2x^5+4x^4+8x^3+16x^2+32x+64)

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factor x^7-128

factor

x^{7} - 128

(x - 2) (x^{6} + 2 x^{5} + 4 x^{4} + 8 x^{3} + 16 x^{2} + 32 x + 64)

Solution steps

x^{7} - 128

Rewrite

128

2^{7}

= x^{7} - 2^{7}

Apply factoring rule:

x^{n} - y^{n} = (x - y) (x^{n - 1} + x^{n - 2} y + \dots + x y^{n - 2} y^{n - 1})

x^{7} - 2^{7} = (x - 2) (x^{6} + 2 x^{5} + 2^{2} x^{4} + 2^{3} x^{3} + 2^{4} x^{2} + 2^{5} x + 2^{6})

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

Simplify

(x - 2) (x^{6} + 2 x^{5} + 2^{2} x^{4} + 2^{3} x^{3} + 2^{4} x^{2} + 2^{5} x + 2^{6}) : (x - 2) (x^{6} + 2 x^{5} + 4 x^{4} + 8 x^{3} + 16 x^{2} + 32 x + 64)

= (x - 2) (x^{6} + 2 x^{5} + 4 x^{4} + 8 x^{3} + 16 x^{2} + 32 x + 64)

(a^{2} + 3 a - 2)^{2}

(- m^{3} n^{- 1}) (m^{- 2} n^{2})

\frac{7}{10} - \frac{4}{5}

103 + 63

3 \frac{6}{7} + (- 1 \frac{1}{7})

What is factor x^7-128 ?
The solution to factor x^7-128 is (x-2)(x^6+2x^5+4x^4+8x^3+16x^2+32x+64)