How to factor a quadratic function
Learn the ac method for factoring and solving a quadratic equation
Timecodes:
again ladies and gentlemen when we're
looking at this when we're looking at a
problem like this basically again what
we want to be able to do is same exact
thing you know I'm not going to do a box
but the same idea is going to apply we
still need to figure out we want to be
able to rewrite our middle term as two
separate values and rather than filling
them in a box we're going to factor by
grouping which we actually talked about
before in this class but either way the
first thing we need to do is do a times
C a times C 9 times 5 negative 5 is
negative 45 and then to add to give us
negative 12
now I get a lot of students that get
stuck in the same miss from going I
don't know you know what to do you know
next the most important thing that I
would say guys even if you get stuck all
right even if you can't figure it out on
your test write down all of the factors
of 45 all right and this isn't that
difficult the way that I want you to do
it is always the obviously you can
always start with 45 times one then just
start working with numbers go from one
now let's say 2 is 2 divisible into 45
no it's not right so then we go to 3 is
3 divisible into 45 yes
so you could say 3 times 15 then work
your way up
what about 4 is 4 divisible in the 45 no
go to 5 it's 5 divisible in the 45 yes
and then we go up to 6 is 6 divisible
into 45 no 7 no hope 8 nope and then I
get back up to 9 which I already know is
divisible so therefore I'm all done so
these are the only factors now we are
multiplying to give us negative 45 so
just think listen to my mind my thought
process it has to multiply to give you
negative 45 and add to give you negative
if you're adding a positive and a
negative number and your answer is
negative should sort the negative or the
positive number be larger in absolute
value the negative number should be
larger
think about it negative five plus three
an absolute value which one is larger
the five or the three the five right so
a larger negative five absolute value of
it plus three is going to equal negative
two right it's going to give you a
negative number so therefore since I'm
adding these two Vout since I'm adding
these two factors and my the sum is
negative then my larger factor has to be
negative and now when I look at this
Ashley which of these add up to give me
negative 12 negative 15 and positive 3
now I'm gonna do just like what I did
last time but I'm not gonna fill it into
a box I'm gonna say 9x squared and then
I'm gonna say minus 15 X plus 3x minus 5
equals 0 does everybody see what I did I
just rewrote the I just rewrote the
equation that's all I did I didn't
change it or do anything else with it I
didn't put it in a box I just rewrote it
just but I mean I showed you guys how to
rewrite this last time and now what we
can do is a prize like factoring
techniques which we call grouping where
you group the first two terms and you
group the last two terms and basically
what we have already done in this class
is we talked about grouping but we also
talked about factoring out the GCF now
all you're simply going to do is factor
the GCF out of each of these expressions
so we look at the first two and say what
do these have in common what is their my
common factor you could say a 3x and
when you factor out a 3x you're left
with 3x minus 5 then I look over here
and I say is there anything I can factor
out of these no so therefore I can
factor out a positive 1 you're always
going to have to factor out something
and if they don't have anything in
common then factor out a positive or a
negative one okay Tyler and then what
therefore we're left with 3x minus 5
now what you guys can see is that the 3x
minus 5 is common between both of these
terms or both of these expressions right
do you guys see I have two expressions
that are separated by addition and
therefore now you factor those out you
factor out what they have in common
which is I don't want to write this like
that so therefore that's 3x minus 5
times 3x plus 1 equals 0 now you can
apply the zero-product property and
therefore I'm not going to show you the
steps to solving and get them all done
now you could do that exact same one by
using the
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