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CCSS.Math: , ,

we're told of the quadratic expressions M squared minus 4m minus 45 and 6 and squared minus 150 share a common binomial factor what binomial factor do they share and like always pause the video and see if you can work through this alright now let's work through this together and the way I'm going to do is I'm just gonna try to factor both of them into the product of binomials and maybe some other things and see if we have any common binomial factors so first let's focus on M squared minus 4m minus 45 so let me write it over here M squared minus 4m minus 45 so when you're factoring a quadratic expression like this where the coefficient on the in this case M squared term on the second degree term is one we could factor it as being equal to M plus a times M plus B where a plus B is going to be equal to this coefficient right over here and a times B is going to be equal to this coefficient right over here so let's be clear so a there's a another color so a plus B needs to be equal to negative 4 a plus B it needs to be equal to negative 4 and then a times B needs to be equal to negative 45 a times B is equal to negative 45 now I like to focus on the a times B and think about well what could a and B be to get to negative 45 well if I'm taking the product of two things and if the product is negative that means that they're going to have different signs and if when we add them we get a negative number that means that the that the the negative 1 has a larger has a larger magnitude so let's think about this a little bit so a times B is equal to negative 45 so this could be let's try some some values out so one in 45 those are too far apart let's see 3 and 15 those still seem pretty far apart let's see it looks like 5 and 9 seem interests so if we say if we say five times if we were to say five times negative nine that indeed is equal to negative forty five and five plus negative nine is indeed equal to negative four so a could be equal to five and B could be equal to negative nine and so if we were to factor this this is going to be M plus five times M I could say M plus negative nine but I'll just write M minus nine so just like that I've been able to factor I've been able to factor this first quadratic expression right over there as a product of two binomials so now let's try to factor the other quadratic expression let's try to factor 6m squared minus 150 and let's see the first thing I might want to do is both six both 6m squared and one fifty they're both divisible by six so let me write it this way I could write it as six actually I'll just write 6m squared minus six times let's see six goes into 150 twenty-five times so all I did is I rewrote this and I just really I just wrote 150 is six times twenty-five and now you can clearly see that we can factor out a 6 you can view this as undistributing the six so this is the same thing as 6 times M squared minus 25 which we recognize this is a difference of squares so it's all going to be 6 times M plus 5 times M minus 5 and so we've factored this out as a product of binomials and some and and a constant factor here 6 and so what is their shared common where does their common binomial factor that they share well you see when we factor it out they both have they both have an mm plus 5 so M plus 5n plus 5 is the binomial factor that they share