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Factoring Trinomials, a = 1 - Concept
Multiplying rational expressions is basically two simplifying problems put together. When multiplying rationals, factor both numerators and denominators and identify equivalents of one to cancel. Dividing rational expressions is the same as multiplying with one additional step: we take the reciprocal of the second fraction and change the division to multiplication.
Factoring is one of the most important skills you're going to learn in your Algebra One course and it's going to show up through the rest of your Math career so it's really important you focus on these times in your school while you're learning how to factor. In these lessons we're going to be looking at how to factor when it looks like x squared plus bx+c. Sometimes this is written with an a right there and we're talking about when a=1.
When a=1, there's a couple of steps you want to do but first I want to show you an example. You're going to be given a problem like this and asked to write it in it's factored form. You're going to be given a trinomial and asked to write it like this. You already know how to do that the other way around, if you're given this, you could FOIL or use an area model to find out this. Let me show you a couple of things to notice. The first thing I want you to notice is that this number right here is the sum of my two constants 3+4 gave me 7. Also look 12, this number here, is the product of my two constants that is super important that pattern is how you solve these problems.
The first thing you're going to do when you're given a trinomial where a is 1 there it is right there that's the one [IB] and you're asked to write it in factored form, first thing you're going to do is look for two numbers whose sum is the middle term which is b, there it is, we want sum to be that and whose product is the constant term. We want our two numbers to multiply to that guy, keep in mind you might have positive and negative numbers that's going to show up later on when you have a negative value right there. Once you have those two numbers write them as factors and FOIL to check your work you're going to see this over and over and over in your Math classes and again it's really important that you remember that the middle term represents the sum and the last term represents the product. If you forget that give yourself a little practice problem on the side of your paper or something write down the product of two binomials, use your foiling and you could figure this out on your own without having to memorize it.