The expression (x4 – 15x3 – 48x2 – 36x) can be factorised as:

To factorize the expression (x4 – 15x3 – 48x2 – 36x), we can follow these steps:

Step 1: Look for common factors. In this case, we can see that all terms have a common factor of x. So, we can factor out x from each term: x(x3 – 15x2 – 48x – 36)

Step 2: Factorize the remaining polynomial. Now, we need to factorize the polynomial (x3 – 15x2 – 48x – 36). To do this, we can try to find its roots by using methods like factoring, synthetic division, or the rational root theorem.

After trying different values, we find that x = 3 is a root of the polynomial. This means that (x - 3) is a factor of the polynomial.

Using synthetic division, we can divide the polynomial by (x - 3) to find the remaining factor: (x3 – 15x2 – 48x – 36) ÷ (x - 3) = x2 – 12x – 12

Step 3: Factorize the remaining quadratic polynomial. Now, we have the quadratic polynomial x2 – 12x – 12. We can factorize this by using methods like factoring, completing the square, or using the quadratic formula.

After factoring, we get: x2 – 12x – 12 = (x – 6)(x – 2)

Step 4: Combine the factors. Finally, we can combine all the factors we found: x(x3 – 15x2 – 48x – 36) = x(x - 3)(x – 6)(x – 2)

Therefore, the expression (x4 – 15x3 – 48x2 – 36x) can be factorized as x(x - 3)(x – 6)(x – 2).