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

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

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

factor

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

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

Solution steps

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

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)

(- 8) (- 8)

- 4 x + 2 (\frac{22}{10}) = 6

2 a (6 a + 1) - 4 a (3 a - 2) < 12

8 x^{2} = x + 3

17 < 9 + x < 35 + 4