Ladies and gentlemen,
if I'm going
to ask you to put it into
standard form, a polynomial
into standard
form, and I'm going
to ask you to find the degree
and the leading coefficient,
the first thing we need to
know is what's standard form?
Yes.
What number is that?
17?
[INTERPOSING VOICES]
Yes.
First thing you know
is, what is even our--
let me just do an example here.
Let's do p x to the m,
where p would be our leading
coefficient, and m is
going to be our degree.
Now, that is where we find it
when it's in standard form.
How we move them
in standard form?
Remember, standard form is
when we take a polynomial,
and we write it in
order from the greatest
degree to the smallest degree.
So I look at this, and I have
a couple of degrees here.
I have 2, 3, there's a 1 there.
Is this in greatest to least--
No.
--order of degrees?
No.
The first thing I need to do is
rewrite it in descending order.
3x cubed plus x squared
minus x plus 27.
Our constant, or number, is
always going to be our last.
Does everybody see that?
That is standard form.
Then, the next
thing I'm asking you
is, tell me what is the leading
coefficient and the degree.
The degree of the polynomial is
going to be the largest degree.
If you guys look at it,
obviously since I rewrote it
from largest to
greatest, we know
the degree of this
polynomial equals 3.
And the leading
coefficient, which
I'm just going to
abbreviate with LC,
is going to be the
leading coefficient, which
is going to be 3.
Anybody have any
questions on that?
OK, so the first--
what?
Why would it be 3 in that--
Because remember, the
leading coefficient
is the number that's
in front of your--
leading term that has
the highest degree.
What you do is you arrange
it from greatest degree
to least degree.
Then that coefficient
of your greatest degree
is your leading coefficient.
See how it kind of leads?
It's like the front, first one.
That's why it's your
leading coefficient.
You need your polynomial
to look at that.
Got it?
Degree and leading coefficient.
So this one actually has the
same, which is kind of cool.
That was one problem
off your homework.
Wow, isn't that?
