1
00:00:00;00 --> 00:00:09;10
I'm going to make one up. How about plus
4 times, I don't now, negative 1, plus 4.

2
00:00:09;11 --> 00:00:13;02
That sounds like a common one. So we'll move that up.

3
00:00:14;05 --> 00:00:18;07
[Can you make that bigger, please?]

4
00:00:22;10 --> 00:00:32;06
Yeah. It doesn't stretch it that much, but does that help at all?
Alright, so, where would you expect to see a zero?

5
00:00:32;07 --> 00:00:33;07
[3]

6
00:00:33;08 --> 00:00:38;04
Positive 3. Can you find that zero?
Where else would you expect to find a zero?

7
00:00:38;05 --> 00:00:39;05
[Negative 1.]

8
00:00:39;06 --> 00:00:39;14
Can you find it?

9
00:00:39;15 --> 00:00:40;12
[Yes]

10
00:00:40;13 --> 00:00:42;05
Where else would you expect to find a zero?

11
00:00:42;06 --> 00:00:43;02
[Negative 4]

12
00:00:43;03 --> 00:00:44;06
Is that all?

13
00:00:44;07 --> 00:00:45;00
[Yes]

14
00:00:45;01 --> 00:00:51;03
OK. And you could figure out positive, negative,
whatever. So you guys have gotten pretty good

15
00:00:51;04 --> 00:01:00;13
At figuring out what's going on if I give this to you and it's called factored form. It factors times each other, it's called factored form.

16
00:01:02;03 --> 00:01:12;13
I'm going to take that exact same equation and I'm
going to click on this word in my menu called expand.

17
00:01:12;14 --> 00:01:21;06
What this is going to do is it's going to take these factors and,
what operation is in between each of those parentheses?

18
00:01:21;07 --> 00:01:22;10
Add, subtract, multiply or divide?

19
00:01:22;11 --> 00:01:23;07
[Multiply]

20
00:01:23;08 --> 00:01:26;09
Multiply. They're all products. So, it's going to do that.
It's going to take the product.

21
00:01:26;10 --> 00:01:31;04
What that button is going to do when I click it,
it's actually going to take the product.

22
00:01:31;05 --> 00:01:35;02
Don't worry about how it's going to do it,
we'll get there eventually.

23
00:01:35;03 --> 00:01:39;03
The computer knows what I want it to do,
I'm asking it to do the math, take the product for me.

24
00:01:41;12 --> 00:01:50;02
That's what you get. The same graph, it didn't
change, I didn't change the function at all.

25
00:01:50;03 --> 00:01:55;07
I just changed the way it looks. Do you
guys agree it looks different? For sure.

26
00:01:58;08 --> 00:02:07;13
Here's the function definition, here's the graph.
Can you find your zeros in this function definition?

27
00:02:14;03 --> 00:02:26;12
I heard a couple mumbles, what were those
mumbles? Not really? OK, I agree. Why not? Mr. Trilli?

28
00:02:26;13 --> 00:02:28;13
[Because it looks weird.]

29
00:02:29;05 --> 00:02:33;13
How do you want it to look? What's
the way that it could be written that,

30
00:02:33;14 --> 00:02:38;08
At least we discovered, can tell you a lot about the graph.

31
00:02:38;09 --> 00:02:40;10
[In that factored form...]

32
00:02:40;15 --> 00:02:43;05
In that beautiful, lovely factored form.

33
00:02:43;07 --> 00:02:49;11
If I give it to you like this, do you think you could
with the same amount of ease as factored form

34
00:02:49;12 --> 00:02:54;01
Find your root as zero, sorry, root's another way to say zero.

35
00:02:54;02 --> 00:02:58;10
So, if I use that I'm sorry, but if I gave
it to you looking like this, would you

36
00:02:58;11 --> 00:03:01;11
With the same amount of ease, be
able to find the zero at negative 4?

37
00:03:01;12 --> 00:03:08;08
Or if I gave it to you like this, could you find
with the same amount of ease a zero at negative 1?

38
00:03:10;01 --> 00:03:18;09
With the same amount of ease. I agree with you though,
I'm sure it's possible, and it is possible. But is it as easy?

39
00:03:18;10 --> 03:03:19;06
[No]

40
00:03:19;07 --> 00:03:21;14
To look at this and say oh there's
going to be a zero at negative 1.

41
00:03:21;15 --> 00:03:22;09
[No]

42
00:03:22;10 --> 00:03:27;11
No, probably not. Or look at this and
say oh that's going to be a zero at positive 3.

43
00:03:27;12 --> 00:03:32;03
Probably not, and I agree with you, it's not that they aren't there

44
00:03:32;04 --> 00:03:38;11
Because they are, and Amy Lynn is right, they are there, you could find them, but probably not with the same amount of ease.

45
00:03:38;12 --> 00:03:43;04
But what about this, if I give it to you
looking like this and I give you the graph.

46
00;03:43;05 --> 00:03:48;05
I'll give you the graph. Can you put it in factored form?

47
00:03:54;03 --> 00:04:03;04
Can you put it in factored form? Here it is not in factored form, but here's the graph that goes with it. Can you put it in factored form?

48
00:04:04;00 --> 00:04:09;04
What would it have looked like, what did
it look like, how can you go from this

49
00:04:09;05 --> 00:04:13;14
Information right here back into the
factored form that I took away from you.

50
00:04:13;15 --> 00:04:28;11
What do you think? Ryan says you can do it. Gina,
do you think you can do it? How so, what do you think?

51
00:04:28;12 --> 00:04:33;13
[By putting the exponents into it.]

52
00:04:34;13 --> 00:04:39;03
By putting what into the exponents?

53
00:04:39;04 --> 00:04:41;03
[To put them back in the equation]

54
00:04:41;04 --> 00:04:49;03
To put the equation back into factored forms.
So,the form that I took away.  Factored form.

55
00:04:50;11 --> 00:04:59;06
[You make the exponents, like, together, or add the X's together.]

56
00:05:02;06 --> 00:05:09;01
You actually can't add any X's together because you're trying
to use the collective property to bring together like terms.

57
00:05:10;07 --> 00:05:14;07
You can't use collective property on those
because they aren't like terms. Ryan?

58
00:05:15;06 --> 00:05:26;04
Look at where your points are on the X-axis, so it's negative
4, so it would be X plus 4, then X plus 1, or X subtracted.

59
00:05:28;05 --> 00:05:41;14
What do you guys think? Remember, I'll give you the graph.
Where did this zero happen? No, on the graph, it happened at

60
00:05:41;15 --> 00:05:43;01
[Negative 4]

61
00:05:43;01 --> 00:05:50;01
Negative 4, so what would that factor have looked like
that said to you guys hey I have a zero at negative 4?

62
00:05:50;02 --> 00:05:51;11
[X plus 4.]

63
00:05:54;13 --> 00:05:56;06
Where did this zero happen?

64
00:05:56;07 --> 00:05:57;10
[Negative 1]

65
00:05:57;11 --> 00:06:05;00
Happens at negative 1. So what would the factor have
looked like that told you hey I have a zero at negative 1.

66
00:06:05;01 --> 00:06:05;11
[X plus 1]

67
00:06:08;06 --> 00:06:11;14
Any others? Should I add another parentheses?

68
00:06:11;15 --> 00:06:12;07
[Yes]

69
00:06:12;08 --> 00:06:14;09
So where did this zero happen?

70
00:06:14;10 --> 00:06:15;07
[3]

71
00:06;16;00 --> 00:06:18;06
So, what would you have seen in factored form?

72
00:06:18;07 --> 00:06:19;08
[X minus 3]

73
00:06:28;00 --> 00:06:31;00
If I hit simplify,will it put it back into factored form?

74
00:06:31;01 --> 00:06:33;02
[No]

75
00:06:33;03 --> 00:06:40;00
No, it doesn't. How about this, then. What's on the board?

76
00:06:40;01 --> 00:06:44;09
[X plus 4, X plus 1, X minus 3]

77
00:06:50;04 --> 00:06:53;00
Come on. Yeah?

78
00:06:53;01 --> 00:06:54;01
Is this good news?

79
00:06:54;02 --> 00:06:55;12
[Yeah]

80
00:06:57;02 --> 00:07:00;00
Yeah? OK good. Very good. Ryan?

81
00:07:00;01 --> 00:07:05;00
[For the graph, does it matter if you
write the factors in that order?]

82
00:07:05;01 --> 00:07:08;03
Class, does it matter what order you write the factors in?

83
00:07:08;04 --> 00:07:08;12
[No]

84
00:07:09;07 --> 00:07:12;02
There's actually a property that tells you why that's OK.

85
00:07:13;05 --> 00:07:14;08
[Oh. Associative?]

86
00:07:14;08 --> 00:07:15;03
Not associative.

87
00:07:15;04 --> 00:07:16;07
[Communitive.]

88
00:07:17;10 --> 00:07:24;01
Communitive. The communitive property multiplication tells
you it's OK, you can write your multiplication in any order.

89
00:07:24;02 --> 00:07:29;02
So you can have this times this times this, that times that times that, it doesn't matter at all thanks to communitive property.

90
00:07:29;03 --> 00:07:29;14
Ok, good good.