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# Factoring higher degree polynomials

CCSS.Math:

## Video transcript

there are many videos on Khan Academy where we talk about factoring polynomials but what we're going to do in this video is do a few more examples of factoring higher degree polynomials so let's start with a little bit of a warm-up let's say that we wanted to factor 6x squared plus 9x times x squared minus 4x plus 4 pause this video and see if you can factor this into the product of even more expressions alright now let's do this together and the way that this might be a little bit different than what you've seen before is this is already partially factored this polynomial this higher degree polynomial is already expressed as the product of two quadratic expressions but as you might be able to tell we can factor this further for example 6x squared plus 9x both 6x squared and 9x are divisible by 3 X so let's factor out a 3x here so this is the same thing as 3x times 3x times what is 6x squared well 3 times 2 is 6 and x times X is x squared and then 3x times what is 9x well 3x times 3 is 9 X and you can verify that if we were to distribute this 3x you would get 6x squared plus 9x and then what about this second expression right over here can we factor this well you might recognize this as a perfect square some of you might have said hey I need to come up with two numbers whose product is 4 and whose sum is negative 4 and you might say hey that's negative 2 and negative 2 and so this would be X minus 2 we could write X minus 2 squared or we could write it as X minus 2 times X minus 2 if what I just did is unfamiliar I encourage you to go back and watch videos on factoring perfect square quadratics and things like that but there you have it I think we have factored this as far as we could go so now let's do a slightly trickier higher degree polynomial so let's say we wanted a factor X to the 3rd minus 4 X square and plus 6x minus 24 and I just like always pause this video and see if you can have a go at it and I'll give you a little bit of a hint you can factor in this case by grouping and in some ways it's a little bit easier than what we've done in the past historically when we've learned factoring by grouping we've looked at a quadratic and then we looked at the middle term the X term of the quadratic and we broke it up so that we had four terms here we already have four terms and see if you could have a go at that all right now let's do it together so you can't always factor a third-degree polynomial by grouping but sometimes you can so it's good to look for it so when we see it written like this we say okay X to the third minus 4x squared is there a common factor here well yeah both X to the third and negative 4x squared are divisible by x squared so what happens if we factor out an x squared so that's x squared times X minus 4 and what about these second two two terms is there a common factor between 6x and negative 24 yeah they're both divisible by 6 so let's factor out a 6 year so plus 6 times X minus 4 and now you are probably seeing the homestretch where you have something times X minus 4 and then something else times X minus 4 and so you can sometimes I like to say undistribute the X minus 4 or factor out the X minus 4 and so this is going to be X minus 4 times x squared x squared plus 6 and we are done