factorise x^3-4x62-11x+2

check your typing, I suspect a typo.

x^3-4x62-11x+2

since ^ is shift-6, I suspect you meant:

x^3-4x^2-11x+2

cubics are not generally easy to solve, so look for easy integral roots first: ±1, ±2

A little synthetic division yields

(x+2)(x^2-6x+11)

Using the quadratic formula, you get
x = 3±2√2

so, the factorisation is

(x+2)(x-3-2√2)(x-3+2√2)

To factorize the expression x^3 - 4x^2 - 11x + 2, we can use a combination of factoring techniques.

Step 1: Grouping
First, we group the terms in pairs:

(x^3 - 4x^2) - (11x - 2)

Step 2: Factor out common terms
From the first pair of terms, we can factor out x^2:

x^2(x - 4) - (11x - 2)

Step 3: Factor by grouping
Now, we group the two sets of terms again:

(x^2(x - 4)) - (11x - 2)

Step 4: Factor out common terms in the second set of terms
We can factor out -1 from (11x - 2):

(x^2(x - 4)) - (-1)(11x - 2)

Step 5: Simplify
Simplifying further, we have:

x^2(x - 4) + (11x - 2)

Step 6: Factor out the common factor
Now, we can factor out the common factor, which is (x - 4):

(x - 4)(x^2 + 11)

Thus, the factorized form of the expression x^3 - 4x^2 - 11x + 2 is (x - 4)(x^2 + 11).