foreign starting our new mini series on factorization it is important to first know what factorization really means factorization is a process where whereby we take a mathematical expression and rewrite it as a product of two factors right so let's get down to the first one but before we start click that Bell subscribe and like let's get into it and so today we are going to be starting probably one of my personal favorite parts of mathematics and it's called factorization and it really goes hand in hand with all the algebra we've been doing up until now all the simplification 3x plus 15. how do I rewrite this as something multiplied by something how do I factorize this expression usually it was easy when I had just 15 on its own and what I'm going to do is I'm just going to see and uh what would happen if I say what are the factors of 3x well we said it's going to be 3 and x and what are the factors of 15 what was 1 and 15 but also 3 and 5. and so now I have to look when I factorize I'm always going to look first so our first step the first type of factorization is called taking out the highest common factor right and so when I try and factorize I'm going to look to take out the highest common factor and so I need to identify what is the highest common factor and so I have a look at these factors that I've written down here what is the common factors and what are the highest common factors if I need to have a look what are the common factors well really there is only one common factor in that is three so I'm going to take that out and what I mean with taking out is essentially I'm going to divide it out of both terms but I do that by saying three I write that first and then I make a bracket open I open a bracket and then would say then I would say well if I take out the 3 if I would divide away that 3 from this first term what would be left behind well 3x I take away the three or I divide it with three that leaves me with just the X and then for the second term that is a positive and what am I taking out I'm taking out A3 see this is my three that's the common factor I've taken out and so if I take out if I divide away a three what remains is that 5 15 divided by three is the remaining factor of that 15 and so I now have this expression but I've Rewritten it as something multiplied by something and you can see that now where previously we had two terms now we only have big picture we only have one term and so I have factorized this successfully because I have Rewritten this expression as something multiplied by something all right and so this is called taking out the highest common factor or the hcf okay I'm going to be keeping an eye out for taking out the highest common factor before we end just remember that these questions might become more challenging but the method stays exactly the same so when you see a more challenging question give it a try but remember follow the steps all right enjoy