Yeah. The concept in this problem is to take the zeros of a polynomial function and to write that polynomial function in order to do that. There are a few things that you will need to know to work with the problem. One thing is that if some number or expression is a zero of the polynomial function, for example, effects of one is a zero, then x minus x. M. One is a factor of that polynomial function. And then also the cons you get paired there, which says that if one complex number is zero. So is it common to get? So let's get started on this problem. We are told that there is a partner number of function of degree five. With these three seals given. Now, since this fall normal function has a degree of five. It can have at most five cereals were given three of them. But we'll be able to tell what the other two zeros are because of this kind get paired there. We know that if x my I'm sorry, we know that if x me back up one more time, we know that if negative I is a zero then its cons get I has to also be a zero. And if one plus I is a zero then it's contradict one minus I is also zero. Now with all of that in mind knowing these five zeroes, then we can write some factors. Okay, F two is a zero, then x minus two is a factor if negative, I is the zero than x minus a negative I is also see well I mean it's a factor of which I can write that is explicit and then also if I is a zero, an x minus I is a factor. If one plus I is a zero and x minus one plus a high is a factor which I can like that as x minus one and minus I. Mhm And if one minus I is a zero then I can say one. I'm sorry X minus one minus side is a factor. Which I can write that as x minus one plus I. So I have the five factors of my polynomial. So to write the polynomial. Yes, I'm going to say that this poem, I'm one of the sun real number. Eight times each one of those factors. So that X nine is chief. Yeah, times X plus high times X nine is uh huh. Trans x minus one minus I terms x minus one plus up. Okay, now, I know that a lot of hours will work to this. Okay, I'm gonna keep the X runs two for just a minute and I'm going to say that X plus I y times x minus I will be x minus x squared minus size square. Mhm. Okay. And then little trick here on this next part now it's both of those have x minus one. X minus one. So I'm gonna take that and go x minus one squared Minnesota scored. Yeah. Okay. Ah A little bit more out to work with this. Okay again some of the number eight times X minus two. This will become X squared plus one. Yeah and this will be X minus one squared plus one. Okay a bit more else will work. A lot of this is just gonna be multiplying these princes together. Big. Okay. The last princess. I'm gonna square this by now. We also have the X square manage to eggs plus one plus one. Mhm. Okay. Yeah it will be X square minus two. U. X. Plus two. Okay now a bit more multiply. Okay if I'm going to buy the first two parentheses together. The first two, that will become X to the third. That is two X squired. Mhm Yeah Plus six. Mhm. Yeah. Yeah. No it's too okay. I got that last process. Okay now it's a lot of multiply. I will start off and I'm going to take the heat to the third times everyone the terms of the second parenthesis. So I will have thanks to the fans managed to X to the fourth plus two eggs to the fired. Yeah. Okay now I'm going to take the negative two X squared terms everybody and I'm going to just kind of keep track of what all I have. I'm gonna wind up my like terms so I've got a negative two X to the fourth. It positive for extra the third. Yeah, negative forex choir. Yeah. Okay now I will take the X times each one of those and again lining up my like terms. I'm going to have extra thyroid man is two X squired plus two eggs. Okay and then lastly I will take the negative two times everybody get lining up negative two X squared plus four X. Name is four and I did like this. I haven't been lined up a little bit easier to collect my like terms. So now I can say that my function is some real number. Eight has that leading coefficient times X to the fifth minus four X to the fourth plus seven. Next to the third 98 K X squared plus 66 minus fault. Okay and that is the polynomial function whose zeros were given and who zeros were able to deduce from the can't you get paired there?