Video: Factor Theorem Video Lecture - Class 9

here let us learn what is factor theorem
but let us see what is factor theorem
with the help of an example
and let us consider P of x equals x
cubed plus 3x squared plus 5x plus 6 and
let us check if X plus 2 is a factor of
X cubed plus 3x squared plus 5x plus 6
now how we can check if X plus 2 is a
factor of X cubed plus 3x squared plus
5x plus 6 is nothing but just find the 0
of X plus 2 which is nothing but
X plus 2 equals 0 x equals 0 minus 2 and
x equals minus 2 so now what we have to
do is substitute
- - in this expression that is in P of X
so that becomes P of minus 2
and here let X plus 2 be X minus a now P
of minus 2 is nothing but minus 2 the
whole cube plus 3 into minus 2 square
plus 5 into minus 2 plus 6 which is
nothing but minus 2 the whole cube is
minus 2 into minus 2 which is plus 4 and
plus 400 minus 2 is minus 8 plus minus 2
the whole square is +4 so therefore it
is 3 into 4 and 5 into minus 2 is minus
10 plus 6 so we have minus 8 plus 12
minus 10 plus 6 which is nothing but
minus 8 plus 12 is plus 4 plus 4 minus
10 is minus 6 and minus 6 plus 6 is zero
so P of minus 2 is 0
or we can say that X plus two is a
factor of X cubed plus 3x squared plus
5x plus 6 so what we can conclude from
this is
I'll make a small note here
factor theorem states that if P of X is
a polynomial of degree N greater than or
equal to one and a is any real number
then X minus a is a factor of P of X if
P of a equal to zero
can relate this note with the example
that I've done here P of X is this and X
minus a is X plus 2 so we've done the
same thing here and we've got P of a
equals 0 so which says that X plus 2 is
indeed a factor of X cubed plus 3x
squared plus 5x plus 6
you