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Welcome to the Georgia Highlands
College Math 97 and Math 99
tutorial videos. In today's
video we'll answer the question
what is factoring?
Well, factoring is the
process of finding what to
multiply together to
get an expression.
So let's take a look at an
example of a polynomial
in its expanded form as
well as its factored form.
If you take the polynomial
form of X^2+7X+12
and you ask yourself the
question what do I have to
multiply together to
get that expression?
You're asking to find
the factored form
of that polynomial.   And
the factored form
of X^2+7X+12 happens to
be (X+3) times (X+4)
Now you might recognize this
from a previous chapter
on distribution and
multiplying polynomials.
So, to check and just
make sure that
this truly is the factored form
of this polynomial you would
simply multiply it back
out using distribution.
So we'll distribute
the X to each term in
the second polynomial
and then I'll come back
and distribute the 3
to both terms of the
second polynomial.
When you multiply X
times X, you get X^2
and X times 4 is
simply positive 4X.
Coming back and
multiplying the 3 by X,
I get positive
3X and multiplying
the 3 by the 4 I get
positive 12. Now you also
learned in a previous chapter
that you should always combine
like terms and when we do so
we end up with the polynomial
X^2+7x+12 which is
exactly what we began with in
our polynomial form.
So the factored form
of this particular
polynomial is (X+3)
times (X+4).
Thank you for viewing
this tutorial video.
If you have any further
questions about
factoring please ask your
Highlands instructor.
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