Final answer:
To factorise [x^2(x+1)(x+2)(x+3)]÷x(x-2), we cancel common factors resulting in (x)(x+1)(x+2)(x+3)÷(x-2), which cannot be further simplified as there are no additional common factors between the numerator and the denominator.
Step-by-step explanation:
To factorise the given expression [x^2(x+1)(x+2)(x+3)]÷x(x-2), we will first simplify it by canceling out common factors and then factor the remaining expression if possible. Let's break this down step by step:
- First, we identify that x can be canceled out from both the numerator and the denominator, as long as x is not equal to zero.
- After canceling out x, we're left with x(x+1)(x+2)(x+3)÷(x-2).
- Next, we see that there's no common factor between the remaining terms in the numerator and the denominator, and x is not a factor of (x-2).
- Therefore, the simplified form of the given expression is (x)(x+1)(x+2)(x+3)÷(x-2).
The expression can't be further factorised since the denominator does not share any additional factors with the numerator, and thus, this is the final factored form.
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