1
00:00:00,627 --> 00:00:03,867
In the following polynomial, identify the terms

2
00:00:03,867 --> 00:00:07,000
along with the coefficient and exponent of each term.

3
00:00:07,000 --> 00:00:12,200
So the terms are the things being added up in this polynomial.

4
00:00:12,200 --> 00:00:17,067
So the terms here, let me write the terms here...

5
00:00:17,067 --> 00:00:20,805
The first term is 3x squared,

6
00:00:20,805 --> 00:00:25,472
The second term it's being added to -8x.

7
00:00:25,472 --> 00:00:27,533
You might say wait, isn't it minus 8x?

8
00:00:27,533 --> 00:00:29,614
And you could just view that it's being added to

9
00:00:29,614 --> 00:00:32,729
-8x, so -8x is the second term, and the third term

10
00:00:32,729 --> 00:00:36,800
here is the 7, it's called the polynomial

11
00:00:36,800 --> 00:00:41,467
poly, it has many terms, or you could view each term

12
00:00:41,513 --> 00:00:45,558
as a monomial, it's a polynomial with only one term in it.

13
00:00:45,558 --> 00:00:48,400
So those are the terms, now lets think about the coefficient

14
00:00:48,400 --> 00:00:49,667
of each of the terms.

15
00:00:49,667 --> 00:00:53,533
The coefficient is what's multiplying the power of x,

16
00:00:53,533 --> 00:00:57,200
or what's multiplying the x part of the term, so

17
00:00:57,200 --> 00:01:00,235
over here, the x part is x squared,

18
00:01:00,235 --> 00:01:02,200
that's being multiplied by three,

19
00:01:02,200 --> 00:01:05,000
so three is the coefficient on the first term.

20
00:01:05,000 --> 00:01:08,467
On the second term, we have -8 multiplying x,

21
00:01:08,467 --> 00:01:10,831
and we want to be clear-- the coefficient isn't just 8,

22
00:01:10,831 --> 00:01:17,392
it's -8, it's -8 that's multiplying x, so that's the coefficient right over here

23
00:01:17,392 --> 00:01:19,200
And here you might say, hey wait!

24
00:01:19,200 --> 00:01:22,517
Nothing is multiplying x here, I just have a 7

25
00:01:22,517 --> 00:01:24,736
there is no x, 7 isn't being multiplied by x.

26
00:01:24,751 --> 00:01:28,892
But you can think of this as 7 being multiplied

27
00:01:28,892 --> 00:01:32,867
by x to the zero, cause we know that x to the zeroth power

28
00:01:32,867 --> 00:01:34,389
is equal to one.

29
00:01:34,389 --> 00:01:37,867
So we would even call this constant, this 7,

30
00:01:37,867 --> 00:01:41,634
this would be the coefficient on 7x to the zero.

31
00:01:41,634 --> 00:01:46,333
So you could view this, you could view this, as a

32
00:01:46,333 --> 00:01:49,400
coefficient, so this is also a coefficient,

33
00:01:49,400 --> 00:01:53,933
so let me make it clear-- these three things are coefficients.

34
00:01:54,256 --> 00:02:00,667
Coefficients. Now the last part, they want us

35
00:02:00,667 --> 00:02:03,623
to identify the exponent of each term.

36
00:02:03,623 --> 00:02:06,603
So the exponent of this first term term is 2,

37
00:02:06,603 --> 00:02:08,764
it's being raised to the second power,

38
00:02:08,764 --> 00:02:10,245
the exponent of the second term,

39
00:02:10,245 --> 00:02:13,725
remember -8x, x is the same thing as x to the first power,

40
00:02:13,725 --> 00:02:16,129
so the exponent here is 1,

41
00:02:16,159 --> 00:02:18,400
and on this last term, we already said

42
00:02:18,400 --> 00:02:21,000
this is 7 is the same thing as 7x to the zero,

43
00:02:21,000 --> 00:02:24,010
so the exponent here on the constant term,

44
00:02:24,010 --> 00:02:29,400
on 7, is 0, so these are, these things right over here,

45
00:02:29,400 --> 00:02:33,667
those are our exponents, exponents.

46
00:02:33,667 --> 00:02:35,600
And we are done.