Name: 多項式のゼロ（多重度）｜多項式グラフ｜代数学2｜カーンアカデミー (Zeros of polynomials (multiplicity) | Polynomial graphs | Algebra 2 | Khan Academy)
Uploaded: 2021-01-14T10:14:28.000Z
Duration: 5 min
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

命令形

- All right, now let's work through this together.

法助動詞 A2

are expressed as a polynomial in factored form.

And factored form is useful when we're thinking

the x-values that make that polynomial equal to zero.

The roots are also evident when we look at this graph here.

So here on the left we have a root at x equals -4.

when x is equal to -4, that means that x + 4

but they have different exponents on them.

The first one has a 2 as an exponent, it's being squared,

while the others have a 1 as the exponent.

Now what we've talked about in other videos,

around a root, like we're seeing right over here

an odd exponent on the corresponding factor.

that means we would see an even exponent.

and, of course, 1 is an odd number and 2 isn't.

you would have a sign change around x equals -4.

these other three choices are still looking good

Now lets move on to the next factor right over here,

and so one way to think about it is you could have

Now, when we look at the choices, or the remaining choices,

we don't see x + 3/2, but we do see something

that involves a 2 and a 3, and so one way to think about it

is just, "Hey, if I just multiply this by the constant 2,

that would get us 2x + 3," well I do see that

right over here, and then the next question is

which is an odd number, while the other one

has an even exponent there, so we can rule

multiplied by some constant, to be one of the factors.

And what's interesting here is we don't see a sign change

around x equals 1, so we would expect an even exponent.

that we would expect, so choice C is looking good.

a situation where the curve would keep going down,

something like that, so we like choice C.

pause this video and try to work through that.

All right, we're going to do the same idea.

Let's go to this first root right over here.

We also have a sign change around x equals -3,

then you wouldn't have a sign change here,

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多項式のゼロ（多重度）｜多項式グラフ｜代数学2｜カーンアカデミー (Zeros of polynomials (multiplicity) | Polynomial graphs | Algebra 2 | Khan Academy)

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