What is factor (x-1)^4+(x-1)^2-6 ?

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

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factor (x-1)^4+(x-1)^2-6

factor

(x - 1)^{4} + (x - 1)^{2} - 6

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

Solution steps

(x - 1)^{4} + (x - 1)^{2} - 6

Let

u = (x - 1)^{2}

= u^{2} + u - 6

Factor

u^{2} + u - 6 : (u - 2) (u + 3)

= (u - 2) (u + 3)

Substitute back

u = (x - 1)^{2}

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

Expand

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

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

Expand

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

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

x (3 t)

sin ({x})

3 a x - 6 + a x m - 2 m

(x + 5) + (4 x^{2})

64 x^{- 6} - 25

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