How to Factor Polynomial

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How to Factor Polynomial

In this video tutorial, I talked about how to factor polynomial using AC method.
Video by shawnkoon

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what’s up guys it’s me Shawn here with
some math tutorial here today and today
we’re going to learn how to factor a
polynomial so let’s get started so the
first thing you have to do is you have
to choose a question so what I did was I
chose this 12x squared plus 5x minus 2
as my practice problem so before we go
into solving what are they mean by
factor factor is pretty much saying you
want to convert this polynomial into the
form that looks something like this
so parenthesis term times parenthesis
term so that’s what’s called factoring
so we’re trying to convert this
polynomial into that factored form so
how do we do that I use this thing
called a AC method and this pretty much
works like charm on every kind of
polynomials if you want to factor and
stuff and if it if this way doesn’t work
out that pretty much means it’s a prime
okay
so let’s get started so before we get
into AC method here we have to know that
in front of what’s x squared it’s called
a so the coefficient in front of x
squared is a and coefficient in front of
X is called B and the last one the
constant is called C and if you have
learned quadratic formula you have to
know how to figure these out right so we
have that a is equal to 12 and B is
equal to 5
and C is equal to negative two right so
let’s use AC method so AC method the
reason we call AC is because we multiply
a and C so let’s do that what’s 12 times
negative 2 yes that’s negative 24 right
so what what we were trying to do here
is we have to find a two numbers that
multiply together to get negative 12 24
but when you combine those two you get a
plus 5 okay so there’s two things we
have to watch out for so let’s start
with number one so 1 times 24 one of
them has to be negative but let’s say I
do this one negative can I get five if I
combine these two No so this one’s not
it how about 2 and 12 if I put negative
here I might get closer to 5 but not if
not quite yet so what we have to do is
we have to move on to next one how about
3 & 8 whoo that seems like it’s going to
work so one of them has to be negative
right so negative 3 plus 8 becomes 5 so
this works out so I know that my AC
method solution is these 2 so now what
we got to do here is we have to break
this middle term here into two different
sections so we have 12
x-square just bring it down okay
and what you’re going to do is you’re
going to take this five and break it
into these two the one we just found so
negative 3x + + 8 X + – 2 because we’re
going to bring this down just like that
okay so now we have four terms here our
next step is to group them so by mean is
we’re going to group two terms like that
all righty
and the third step here is we have to
factor out the common numbers from each
of these terms so out of these two
notice I can pull out an X right because
X is in common but also I can pull out
on 3 because 3 goes into 12 so I’m going
to factor out 3 and X at the same time
so I get 4x left over – one like that
and from here I can factor out a 2 so
I’m going to put factor out + 2 and I’m
left over with 4x – 1 nice so how do we
know if we can make any mistakes we can
tell by looking at these two terms if
these two terms matches up that means we
are good
okay so now the last step here is we
have to combine these two into one and
we have to combine these two into one so
3x + 2 becomes our 1 term and 4x plus a
minus 1 becomes our second term and that
is our answer so yeah that’s how you use
AC method to solve a factoring problem
you

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