Name: Zeros of polynomials (with factoring): common factor | Polynomial graphs | Algebra 2 | Khan Academy
Uploaded: 2020-03-27T17:33:18.000Z
Duration: 3 min 32 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

- So we're given a p of x, it's a third degree polynomial,

The imperative

and they say, plot all the zeroes or the x-intercepts

of the polynomial in the interactive graph.

And the reason why they say interactive graph,

this is a screen shot from the exercise on Kahn Academy,

where you could click and place the zeroes.

But the key here is, lets figure out what x values make

So the key here is to try to factor this expression

right over here, this third degree expression,

because really we're trying to solve the X's

for which five x to third plus five x squared

is a common factor across all of the terms.

It looks like all of the terms are divisible by five x.

if we take a five x out of five x to the third,

If we take out a five x out of five x squared,

And if we take out a five x of negative 30 x,

we're left with a negative six is equal to zero.

And now, we have five x times this second degree,

the second degree expression and to factor that,

let's see, what two numbers add up to one?

And their product is equal to negative six.

And let's see, positive three and negative two

times x minus two, and if what I did looks unfamiliar,

I encourage you to review factoring quadratics

and that is all going to be equal to zero.

And so if I try to figure out what x values

are going to make this whole expression zero,

or the x value that makes five x equal zero.

zero times anything else is going to be zero.

Well if we divide five, if you divide both sides by five,

The other possible x value that would make everything zero

is the x value that makes x plus three equal to zero.

And then the other x value is the x value that makes

Add two to both sides, that's gonna be x equals two.

We have identified three x values that make our polynomial

equal to zero and those are going to be the zeros

We have one at x equals, at x equals two.

but the reason why folks find this to be useful is

it helps us start to think about what the graph could be.

So the graph might look something like that,

And to figure out what it actually does look like

we'd probably want to try out a few more x values

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Zeros of polynomials (with factoring): common factor | Polynomial graphs | Algebra 2 | Khan Academy

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