Factoring: Special Cases Part II - Problem 3
Here I have a polynomial with four terms so I’m thinking I’m going to want to try factoring by grouping. In order to do factoring by grouping the first thing I’m going to look for is to make sure my polynomial is in standard from. This guy you might notice is not in standard form because these two terms are flip-flopped.
I need the exponents on x to go in decreasing order. So my first step is going to be to rewrite it so that it is in standard form there it is. Next thing I’m going to do for factoring by grouping is split it into two different groups. I was really careful to draw my lines so I could see that negative signs still attached to the 15x piece. Let's look at this group and make sure I can find a monomial that goes into both of these terms.
The number that goes into 6 and 8 is 2 and then I’m going to have x squared that goes into both of those, I’m left with 3x take away 4 let's look at this. I'm looking for a number that multiplies into 15 and 20 so the first thing that comes to mind is 5 and I would need -3x plus 4 oh-oh! Look you guys my binomials are different.
They are really close but they are different, the way they are different is by this negative sign what happened is that this is being multiplied by -1 in order to get to that. So if you don't remember anything else from this video I hope you guys pay really attention right here. My binomials are tiny but different. So instead of factoring out +5 here I’m going to factor out -5 and then it’s going to work out I’ll show you what I mean.
If I pull out -5 right there, then I would have +3x take away 4 that's good that's what I was looking for. That's the trick when you are factoring out by grouping you want to make sure that your signs the positives and the negatives are exactly the same. So I think this is my final answer before I move on I want to make sure that neither one of these binomials can be factored any further.
Like if this had been 2x minus 6 then I can factor out a 2. But in this situation I can't factor out any other monomials so I’m all done. The way I would check this is by Foiling I’m not going to do that now because I know you guys are good Foilers but I want you to remember that when you are factoring by grouping first make sure it's in standard form then when you are doing your factoring of each of the groups make sure the signs, positives and negatives, are exactly the same on your greatest common factor binomial.