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We talked about how to
go from factored form into

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What's called
standard form,

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But expanded form, yes?
And how did we expand it?

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What did we use?

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[Distribution]

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Distribution, distributive
property. So, if we did that,

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Uh, I don't know what you
want to be A or B or C,

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I guess it doesn't matter.

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How about this is B and C,
and that's A, just for fun.

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K, so if chose that this
is my A, B, and Cs,

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How would this get
distributed. Mike?

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[AB because, or X times X
plus 3 plus 4 times X plus 3]

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OK, good. I decided that
I wanted to distribute

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the X plus 3, so I did.

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You could have done it
the other way of course,

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But you guys know that.

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So all right, then we're here.

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OK, you distribute again.

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Yeah, so, go ahead
and do this,

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You said X to the
second. Good.

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Danielle B, distribute
this for me.

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[Plus 4X plus 12]

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Good. And, Sabrina? Help.

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[X squared plus 7X]

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OK, can I ask you where
you got the 7X?

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[I added 3X plus 4X]

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OK. So, just humor
me for a second.

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She collected the
3 plus 4, yes?

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And actually, humor
me on this as well.

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Where did the
12 come from?

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So, I'm just purposely not

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[inaudible] this
would be a 7X,

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And it came from collecting
the 3 plus 4, yes?

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Yes, so the name
of the game is...

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Comes from this,

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So this I think we've
come to decide is.

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At least so far, a more
useful case than having

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This expanded form
down here.

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And to be honest a lot of
times they will give it to you

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Already expanded. I was giving you a lot of

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Factored forms because that's how we

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Started talking about zeros.

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But a lot of times, they will give it to you in

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what's called standard
or expanded form.

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And so, it's going to be
beneficial to know how to

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get back to factored
form because

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We like plotting our
zeros, as Julie said.

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So, here's expanded form,
here's factored form.

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Any observations?

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Sabrina?

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[The fact that there's an
X squared comes from]

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[The fact that there
are 2 factors]

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Good. The fact that there's an X squared comes from

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The fact that there
are 2 factors, good.

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Each had an X and
an X, good good.

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So, she figured out that if you break your factors X

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Plus some number and
X plus some number,

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You will get that X squared back if you distribute. Good.

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What else? Gina?

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[If you add 4, and 3 is 7,
and 3 times 4 is 12]

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OK, so, Sabrina gave us insight as to the fact

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That we're going to need
an X and an X

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in each quantity,
in each factor.

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But, when it comes down to it, aren't those the numbers

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That you end up wanting
almost the most?

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Because those are
going to be the values

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That help you find
those zeros.

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So Gina says, all
right, if I look at

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These two numbers,
they get, she said

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[7]

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Well, added, yeah, added to make this middle term

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Of 7X and multiplied
to make that

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Constant term on
the end a 12.

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What do you guys think?
You guys see that?

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So I wonder if that's
always the case.

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