Tip:
Highlight text to annotate it
X
♪Music♪
Welcome to the Georgia Highlands College Math97 and Math99
video tutorials. In this video segment we'll be answering the
question how do you factor a trinomial with a leading
negative term? Well the first thing you want to
do is factor out the negative GCF which is going to change all
the signs of the terms in your trinomial. Then you'll factor
the remaining trinomial within the parentheses.
Finally you'll check this through multiplication. Let's
take a look at an example.
We'll start with the example -16X^2+16X+96.
Notice that the A coefficient on the X^2 term is negative
so we want to find the negative GCF to
factor out before we begin our other factoring methods and in
this case each of these terms contains the factor 16.
So 16 is the GCF. -16 is the negative GCF.
So that's what I'll be dividing out of each term is -16.
And when I divide -16X by -16 I end up with positive X^2.
Positive 16X divided by -16 gives us negative X.
And positive 96 divided by -16 is -6.
So now we factored out the negative GCF and only have left
to do is factor that trinomial whose understood leading
coefficient is 1 using the method that we've learned in
previous videos. So we'll ask ourselves the question what do
we multiply to make-6 but add to make -1 now that
negative wine that were adding to make comes from the BX term
that understood -1. So in thinking about the factors of
-6 we should be able to come up with -3 times (+)2 gives -6.
And -3 plus (+)2 gives -1. So we still have our factor
of -16 that must join the other part we're factoring
and we can set up our space to finish factoring the
trinomial from inside the parentheses. So from the work we
did with our factoring teepee we see that (X-3) and (X+2) are
other factors. So the factored form of -16X^2+16X+96
is -16(x 3)(X+2). And we need to check that
with the multiplication. In the last video segment we talked
about how to properly multiply three factors together so the
first thing we'll do is distribute this -16 into the
first set of parentheses. We'll get that result and multiply it
by the (X+2). (-16X+48)(X+2). Now we have distribution of
each term in the first set of parentheses to
each term in the second set of parentheses.
-16X times is -16X^2 -16X times 2 is -32X.
Coming back and distributing the 48 we have 48 times X.
which is positive 48X. And 48 times 2 which is positive 96
Combining like terms, we get -16X^2+16X+96.
Which as you can see is the same polynomial we
began with. So the factored form of -16X^2+16X+96 is
-16 (X-3)(X+2). I hope this has been
helpful for you in understanding how to factor a trinomial with
a leading negative coefficient. If you have any other questions
about this concept or method, please contact your
Highlands instructor.
♪Music♪