Factorise fully x^3 - 10x^2 + 16x

The first thing we notice is that there is a common factor of x. Thus we can factor it out and get:x(x^2 - 10x + 16)
This becomes much easier to deal with. We now focus on the equation in the brackets.We need to find 2 numbers that sum to make -10 and multiply to make +16. The only way this is possible is if both numbers are negative (we need at least one negative number to make -10 and we know negative * negative = positive so we need 2 negative numbers). So let's list these factors of +16:-1 -16-2 -8-4 -4-8 -2-16 -1
Of these, the only one that sums to -10 is -2 -8 (or -8 -2). Thus x^2 - 10x + 16 factorises to (x - 2)(x - 8)
Putting it all together,x^3 - 10x^2 + 16x = x(x - 2)(x - 3)