Factorising Quadratic Trinomials using Negative Common Factors


What’s the common factor guys? I know a lot of you will say three but in order to make this into a monic polynomial. We should take out negative three.
Monic means one not negative one so you can’t have negative one as well. So if I take out negative three the whole thing with a 3 negative as well I have positive x squared and this will be negative 5x and this will change into a positive 4. So all the signs switch around because I took the negative out.

So now let’s try and factorize this middle part, I’ve got x and x, 4, I think I’ll use negative 1 and negative 4 because negative 1 minus 4 makes negative 5. So let’s just check that one negative x that’s negative 4x and if you put them together you get negative 5x which is what we have, so we’ve got the right choice. So we keep out negative three and then we put out an x minus one and x minus four here okay? And that’s it just keeps the common factor out.

Guys, what are you going to factorize this time by?
None of you are saying 2, must be negative 2, okay? To keep that negative out as well so we’ve got x squared minus 3x minus 4 left-hand sides so make sure you remember to switch around all the other signs as well. So let’s go factorize inside the bracket so I’ve got x and x and 4,

I’m gonna use plus 1 and minus 4 because I know that plus-minus makes negative and 1 minus 4 is negative 3. Let’s check that is x that is negative 4x and then you put them together x minus 4x is negative 3x which is the right one. So it’s going to be negative 2 outside with x plus 1, x minus 4. In case it’s very repetitive there’s nothing really hard about this one.


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