Factorise
x
(x-1) (x-2)(x-3) +1
Answers
Answered by
1
Answer:
Step-by-step explanation:
My answer is written assuming question is x^3 + (1/x)^3 - 2. Feel free to correct me if I am wrong.
To factorize x^3 + 1/x^3 - 2, take LCM of the expression.
Expression becomes, (x^6 - 2 x^3 + 1) / x^3. Now numerator is easily factorisable as (x^3 - 1)^2
So final expression is (x^3 - 1)^2 / x^3.
Edit-1: As requested by dropa, for further factorization with real coefficients, we can use
x^3 - 1 = (x - 1)*(x^2 + x + 1)
So (x^3 - 1)^2 / x^3 = [(x - 1)^2 * (x^2 + x + 1)^2] / x^3
This cannot be factorized further with real coefficients. However if complex coefficients are allowed, we include imaginary cube roots of unity.
i.e.,
x^2 + x + 1 = (x + w)(x + w^2), where
w = [1 + i√3]/2
Hope it helped !
Similar questions