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### Factorize completely x^3 - 6x^2 + 11x - 6

Let f(x) = x^3 - 6x^2 + 11x - 6.

Try x = 1：   f(1) = 1 - 6 + 11 - 6 = 0

So x - 1 is a factot of f(x).

Try x = 2：   f(2) = 8 - 24 + 22 - 6 = 0

So x - 2 is a factot of f(x).

Try x = 3：  f(3) = 27 - 54 + 33 - 6 = 0

So x - 3 is a factot of f(x).

Thus         x^3 - 6x^2 + 11x - 6 = (x - 1)(x - 2)(x - 3)

3 years ago

Answered by Kai, an A Level Maths tutor with MyTutor

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