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).