Verified answer

Use synthetic division

possible root = 2, because 2^3 - 2^2 + 2 - 6 = 8 - 4 + 2 - 6 = 0

2 | 1 -1 1 -6

...|___2_2_ 6

.... 1 1 3 0

2 is a factor, because the remainder is 0.

(x-2)*(x^2 + x + 3)

(x^2 + x + 3) cannot be factored

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To use synthetic division, take the factors of the last term of the polynomial and them by the coefficient of the first term

6 = -6, -3, -2, -1, 1, 2, 3, 6

first term is 1 in this case.

Divide the last term factors by the first term factors.

Find the value that when plugged in makes the polynomial equal 0, in this case 2.

Once you find that, you can start whittling the polynomial down. Once you hit ax^2 + bx + c you can use the quadratic formula to solve for the rest.

x³ - x² + x - 6 = (x-2) (x^2+x+3)

:)