What is factor x^3+1-x^2-x ?

The solution to factor x^3+1-x^2-x is (x-1)^2(x+1)

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factor x^3+1-x^2-x

factor

x^{3} + 1 - x^{2} - x

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

Solution steps

x^{3} + 1 - x^{2} - x

Write in the standard form

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

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

Factor out

x^{2}

from

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

Factor out

- 1

from

- x + 1 : - (x - 1)

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

Factor out common term

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

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

Factor

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

= (x - 1) (x + 1) (x - 1)

Apply exponent rule:

aa = a^{2}

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

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

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