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Current time:0:00Total duration:4:58

Video transcript

so we're told to factor the polynomial below by its greatest common monomial factor so what does that mean so we have these two terms and I want to figure out their greatest common monomial factor and then I want to express this with that greatest common monomial factor factored out so I can we tackle it well one way to start is I can look at just the constant terms I can look it or not the constants the coefficients I should say so I have the 8 and the 12 and I could say well what is just the greatest common factor of 8 and 12 the GCF of 8 and 12 and there are a lot of common factors of 8 and 12 they're both divisible by 1 they're both divisible by 2 they're both divisible by 4 but the greatest of their common factors is going to be 4 so that is equal to 4 so I could let me just leave that there and then we could think about what is let me actually write it right over here I'll put a 4 here and now we can move on to the powers of X we have an x squared and we have an X and we can say what is the largest power of X that is divisible into both x squared and X well that's just going to be X x squared is clearly divisible by X and X is clearly divisible by X but X isn't going to be isn't is it going to have a larger power of X as a factor so this is the greatest you could do this is the greatest common monomial factor of x squared and X now we do the same thing for the Y's so we have a Y and a y squared if we think in the same terms the largest part of Y that's divisible into both of these is going to be just Y to the first power or Y and so for X Y is the greatest common monomial factor and to see that we can express each of these terms as a product of 4 X Y and something else so this first term right over here so let me pick a color so this term right over here we could write as 4 X Y that's that one's actually that color is hard to see let me pick a darker color we could write this right over here as 4 XY times what and I encourage you to pause the video and think about let's see four times what is equal is going to get us to eight well four times two is going to get us to eight x times what is going to get us to x squared well x times X is going to get us to x squared and then Y times what is going to get us to Y what's just going to be y so for X Y times two x is actually going to give us this first term so actually let me just rewrite a little bit differently so it's for X Y times 2x is this first term and you can you can verify that four times two is going to be equal to eight x times X is equal to x squared and then you just have the Y now let's do the same thing with the second term and I just want to do this to show you that they vote that this is their largest common monomial factor so the second term and I'll do this in a slightly different color do it in blue I want to write this as the product of four X Y and another and another monomial so four times what is 12 well four times three is 12 x times what is X well it just going to be one so we'd have to write up times one here and then Y times what is Y squared it's going to be Y times y is y squared and you can verify if you multiply these two you're going to get 12x y squared four times three is twelve you get your X and then Y times y is y squared so so far I've written this exact same expression but I've taken each of those terms and I factored them into the greatest common monomial their greatest common monomial factor and then whatever is left over and now I can factor the 4 X Y out I can actually factor it out so this is going to be equal to if i factor the 4 x wise out you can kind of say i undistribute the four XY if i factor it out this is going to be equal to four XY x times two x two x plus when i factor 4 it's live from here I get the three Y leftover plus three why and we are done and you can verify it if you if you were to go the other way if you were to distribute this for X Y and multiply it times 2x you get 8x squared Y and then when you distribute the 4 X Y onto the 3y you get the 12 X Y squared and so we're done this right over here is our answer that the answer is going to be 4 X Y which is the greatest common monomial factor x 2x plus 3y