Name: Zeros of polynomials (with factoring): grouping | Polynomial graphs | Algebra 2 | Khan Academy
Uploaded: 2020-03-27T17:19:30.000Z
Duration: 4 min 55 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...

and it says plot all the zeros or x-intercepts,

of the polynomial in the interactive graph,

and the reason why it says interactive graph

and on Khan Academy, you'd be able to click on points here

and you can either delete them and put 'em someplace else,

so I'm just going to draw on top of this.

But the main goal is, what are the zeros of this polynomial

and then you just to plot it on this graph,

All right, now to figure out the zeros of a polynomial,

you would essentially have to figure out the x values

that would make the polynomial equal to zero.

Or another way to think about it is the x values

minus nine x minus nine is equal to zero.

The first thing I look for is are there any common factors

to all of these terms, and it doesn't look like there is.

and when I think about factoring by grouping,

I would look at the first two terms and I would

and I would say, is there anything I could factor out

or what's the most that I could factor out

and then what's the most that I could factor out

something similar once I've done that factoring.

Now, what I mean is, for these first two,

and these first two terms become x squared times x plus one,

so I could rewrite it as negative nine times x plus one.

if we view this as our now our first term

we can see that x plus one is a factor of both of them.

and I'll do that in this light blue color,

actually let me do it with slightly darker blue color.

you're left with x plus one times x squared,

because now we have a difference of squares.

X squared minus nine, this is going to be equal to,

so I have x plus one, and then the x squared minus nine,

I can write as x plus three times x minus three.

If any of what I'm doing feels unfamiliar to you,

if that first factoring feels unfamiliar,

I encourage you to review factoring by grouping,

I encourage you to look at factoring differences of squares.

But anyway, all of that would be equal to zero.

Now, if I have the product of several things equaling zero,

any, if any one of those things is equal to zero,

that would make the whole expression equal to zero.

and once again, I'm gonna do that in darker color,

that of course is x is equal to negative one.

And that of course is x is equal to negative three,

going to be whatever x value makes x minus three equal

at any of these x values will be equal to zero.

So we can plot it here on this interactive graph,

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

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