To factorise 3x²y³z - 2x³y² - xy²z, we can look for common factors among the terms.
First, we can see that both terms have a factor of xy², so we can factor that out:
xy²(3x yz - 2x² - z)
Next, we can see that the expression in the parentheses is a trinomial. To factor it further, we can look for two numbers that multiply to 3xz and add to -2x. The only pair of factors of 3xz is 3xz and 1xz (or -3xz and -1xz), so we can try factoring by grouping:
xy²(3xyz - 2x² - z) = xy²(3xyz - 6x² + 4x² - z)
= xy²(3x( yz - 2x) + 4x² - z)
= xy²(3x( yz - 2x) - z(4x - y²))
Therefore, the fully factorised form of 3x²y³z - 2x³y² - xy²z is:
xy²(3x( yz - 2x) - z(4x - y²))