Why is it that when I am asked to factorise 3x^2-13x-10, I am not able to cancel two of the x's so that the answer is 3x-13-10?

This is because to be able to cancel an 'x' in the equation the 'x' needs to be multiplying every constant. For example, if you were to think of the 'x' as equaling 3 in the question above, then the 10 would also needed to be divided by 3. However, this does not help when you are factorizing as the aim is to have a constant in each bracket, that when multiplied equals -10, eg +/-2 & -/+5, or +/-1 & -/+10. I would then proceed to work through the equation with the student giving the answer (3x+2)(x-5). If the student was still struggling I would help them understand factorising using an easier equation, perhaps one that starts with x^2, instead of a constant and then x^2 like the example.