in this video i'm going to show you guys how to factor a five term polynomial and i'm going to
work out these two examples right here for you guys you can see they look very similar right
so i have two remarks i want to make before we do these two questions first not all the
factor polynomials are factorable we can only do the ones that are well decided and second remark
is that they will be hard anyways let's focus on this one first as you can see we have five
terms it's a good habit we should check to see if we can factor any gcf from all these terms
but no because first of all the last one is just one and then for the numbers there's no other
number besides one right so no gcf and right here whenever we're trying to factor things out
that has more than three terms and that means if we have four five six or even more we should
do this by grouping this right here we have five terms and we have a few ways to group them right
maybe you can group the first two together and then the second
three like this or the first three like this and then the last two like that
and we just have to try it and i just mentioned it it's going to be hard right
let's look at this and let's think about this carefully i'm going to group the first
three terms like this well why because first of all i can factor x squared right
that's good and without being done let's group the last two like this then and let's see what we get
for these three terms we can factor out x to the second power and then for the left
over well for the first term originally it was x plus four but we took the 2 out right so we have
x squared and then we add the 2 we have x 3 but if you factor out 2 of them so x were first
the x squared was out so plus 1 just like this right so that's the progress and
then let me write down plus x plus 1 what can we factor out nothing too much right
so let me just factor out a 1 and then let me put a parenthesis around this x plus one like that
well this entire parenthesis in black and this entire parenthesis in black they are not the same
so we cannot factor things out yet right however as i told you guys earlier these questions are
well designed it look at this right here x squared plus 2x plus 1. what can we do with it well we can
factor this and this is going to give us x plus 1 times x plus 1. i know this is the same as
x plus 1 squared but it would be better for me to write them down separately like this for now
and we see that i have an x plus 1 right here and this is also an x plus one that means i can factor
out one of this factor out right so we will do that let me factor out x plus one and then let me
put down the left over in this big parentheses for the first part here okay before this addition sign
we took one of the x plus one out that means we have the x squared right here still left
and then we have another one right here so let me put that down this right here
is the one that we still have left x plus one put on black and then we add this one right
and you see we have a factor times another thing we factored it but then the usual deal
is that at the inside here let me just try to combine like terms let me just distribute this
into the parenthesis x squared times that and actually we're done we have an x plus
one all the way in the front and then the big parenthesis is going to give us x squared times x
that's x to the third power x squared times one is plus x squared and then we have a plus one
parenthesis times parenthesis look at that this is how we can factor a phantom polynomial right
how would you do the second one [Music] i am going to group the first two layers
for this one and then we can drag this edge one right and then i'm going to bring this up
[Laughter]
okay