Solving problems on Middle-term Factorization : 2 - Factorisation Video Lecture - Class 8

now I will take those that we have been
taking all positive terms right so
polynomial airheaded the examples one
through four we have taken all of the
positive terms how about let us take
some negative terms you have it now in
this case a Mary Jo a here that is one
right is one and hamari Josie term here
that is minus six
sohe marriage' easy Bunty here EC is 1
times minus 6 which is equal to minus 6
naturally so those two become a minus 6
key factors linear right so so got minus
60 factors occur have so it's the
harissa goes to so you can basically do
you can actually do it like this 1 times
minus 6 right minus 1 times 6 2 times 3
basically two threes are 6 you can take
the first one as minus 2 times 3 and for
the second one you can take 2 times
minus 3 right so those so this is
because a happy Joe what we did those to
us basically you're at the helico abuja
a negative term cobalamin right you just
write the number and you just try to
find out the factors so basically just 6
house key factors have 1 6 2 & 3 but
because now you're happy we have to
consider the negative term minus 6 so
away your paheli combination and there
can be actually two different ways we
can write it we can take plus 1 and we
can multiply by minus 6 to get minus 6
because plus times minus is negative
similarly for the other combination we
can write minus 1 x plus 6 so similarly
those that we can write minus 2 times 3
& 2 times minus 3 so we have got these 4
different factors combinations right so
i actually take the hand which is the
one you say add car necessary we will
get minus 5
Agora in the look at the hodo stone what
will happen 1 minus 6 is actually equal
to minus 5 so how many we don't have to
look for the rest those though because
we have already found out our factors so
Abby hammock Akane have we go back here
and we write X square we will write plus
X which is plus 1 X right one we don't
write it but you're happy term 1 is your
first one minus six is your second one
6x minus 6 so homologa factors have 1
and minus 6 these are the two he says
absalom the - where could we have broken
it down okay no no terms may say we take
the common X is our common term so we
get X plus 1 and IV in dono terms may
say we take minus 6 as a common term so
you get X plus 1 y plus 1 because you
have to - successor - 6 x + 1 is minus 6
so ah be in dollar terms mess if we take
the common term so your X plus 1 is
common so of X plus 1
look the vesica okay and then to get the
first time we multiply by X to get the
second term we multiply by 6 so those
are Hamlet a car now this time that to
factorize x squared minus 5x minus 6 you
say we can factorize it using middle
term and we get X plus 1 times X minus 6
now actually also let us take the next
example now this time we have a is equal
to 1 right coefficient G have a ogun a
de de jeunesse a you know it is 1 and
then C joha hamari that is minus 16 so
again if you have like this then it
means to ugly AC here that will be plus
1 times minus 16 that will be equal to
-16 so here Bandidos the minus 16 now
let us just go ahead and write the
factors of 16 right so 16 K factors have
you can write 1 times 16 you can write 2
times 8 right you can write 4 times 4 so
so app si Kathy you can write 16 now
because you have a negative 16 so you
can have minus 1 times 16 or you can
have 1 times minus 16 right because both
are equal to -16
similarly those 4 in this case you can
take minus 2 times a minus 16
or you can write 2 times minus 8 and in
this case also you can write basically
you can take one term as minus for the
other term is 4 right so so so 4 minus
16 we have these are the combinations 1
2 3 4 & 5 so I may take me have each
combination those the will give us this
minus 6 so grab a healthy combination
later ho so minus 1 plus 16 will be plus
15 if you take a look at the second
combination minus 2 plus 8 will be plus
6 but you have to have minus 6
now if you look at the second
combination minus 4 plus 4 will be
actually 0 look at the fourth
combination 1 plus 1 minus 16 is minus
15 if you look at the last combination 2
minus 8 is minus 6 so this means this is
the one that we are looking for right so
I got up to minus 8 consejo you get
minus 6 so we will write it this way X
square minus 6 right -6 totem hamari we
want to write it as 2x minus 8 so we
will write it as plus 2 X minus 8 X
minus 16
so are we in dollar terms miss also we
take the common term so X is our common
term to get x squared it will be x times
X plus to get to X we multiply X by to
IV in dollar terms maybe take the common
term minus 8 is a common term minus 8
times X is minus a minus 8x and to get
minus 16 we have to multiply a by 2 but
it should be plus 2 because I got AB
minus 2 so multiply car to her minus 8
minus 2 will be plus 16 but you have -
so you have to multiply 8 minus 8 by
plus 2 and then those go up they forget
Kyogre up in dollar terms miss a common
later huh clearly X plus 2 is a common
term and then to get the first term you
have to multiply this by X to get the
second term after I say multiply
curly-head with -8 so those are x
squared minus 6x minus 16 a graph is a
factor ice cut the haul your answer is X
plus 2 times X minus 8 so those are we
have seen lot of examples actually we
have seen 6 precise examples you have a
key middle term factorization have
classical - hey and how do we how do we
break it down now H is also before we
just wrap up hum of the share can watch
out the hair after the high up that key
remainder theorem care factor theorem
cure other octopus extra time here and
if you are in doubt up very quickly you
can take a look at any of these factors
and up very quickly you can apply
remainder theorem and check your answer
so what we mean by that is mandated at
this very last example agar hum a if I
if we want to check he if these are the
two factors are not akumal of a
remainder theorem a dosto
humming alcohol a hickey agar aapke paas
a polynomial px he right again Agora
passaic polynomial GX a divided consejo
where manager GX is a linear polynomial
of the form X minus a agora hota hai
gusto then right then in that case the
remainder is given by P
right so other epic polynomial px
Kodiaks I divide consejo and GX is of
the form X minus a is a linear
polynomial then the remainder Hoagy of
this will be PE and after a factor
theorem cerveja dosto he again if you
have if you have a linear factor like
this again if this is a factor of any
polynomial then PA will be equal to zero
right
in other words factor theorem endoscopic
ahead ki agar X minus a if this is a
factor of a polynomial px right then P a
should be equal to zero so Samara point
you happy other octopus extra time here
and if you want to just check make sure
that your factors are indeed correct
so our cackles cackles at the hook you
can simply try to find out the value of
P a and see if it is indeed 0 so we will
just do one example probably again if
you want to find out this so P 8 right I
think we will run out of space you happy
but let us see if we can just fit this
in
so P 8 those though yeah a polynomial
Hemery PX or again a value call me happy
eight so it will be eight squares at 64
right it will be eight square which will
be 64 then 6 times 8 is 48 minus 48
minus 48 and then you have minus 16
minus 16 okay wrap is a solve cut a hole
you will see that let us see so minus 48
and minus 16 is actually 64 so you have
64 minus 64 which is equal to 0 system
of the via who are those 30 this is
indeed a correct factor and then
similarly you can put X equal to minus 2
yeah happy and and see you know and then
our notice curvy this will also be equal
to 0 so those who hopefully are
following us along and like we always
say we serve I'll take a question happy
a beta checker may you send us a comment
we'll be more than happy to answer that
for you
yeah