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}), n i s o dd

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)

(k + 1)! - 1 + (k + 1) (k + 1)!

(4 + 2 i) + (- 12 - 2 i)

- 3 \cdot (- 4)

(x + 4) (x^{2} - 4 x + 16)

(2 x^{2} + 3)^{2}

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)