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QUESTION 17By using the rational zeros theorem what are all of the potential rational zeros of f(x) = ~x3 -7x2+3x+22+1*1,+211,* 2QUESTION 18Sketch the graph of: f(x...

Question

QUESTION 17By using the rational zeros theorem what are all of the potential rational zeros of f(x) = ~x3 -7x2+3x+22+1*1,+211,* 2QUESTION 18Sketch the graph of: f(x) = (x-3)x - I)(x + 1)2

QUESTION 17 By using the rational zeros theorem what are all of the potential rational zeros of f(x) = ~x3 -7x2+3x+2 2 +1 *1,+2 11,* 2 QUESTION 18 Sketch the graph of: f(x) = (x-3)x - I)(x + 1)2



Answers

List the potential rational zeros of each polynomial function. Do not attempt to find the zeros. $$ f(x)=3 x^{5}-x^{2}+2 x+18 $$

We want to use the rational 00 to help us by all the possible rational zeros for polynomial. Well, remember, the rational zero room says that this will be the factors of P over the factors. O Que. Which P is our constant term, and Q is our coefficient of our leading term. Now we have a plus or bias on the outside here, so we look at the factors of two. So even though it's negative, too, is not going to matter, since we have plus or minus on the outside. So we just want to look at the factors of to which end up being one and two. Now, what about the factors of Q's? So that's 18. It was gonna be one and 18 2 and 93 and six and others to be all of them. Now we're going to go ahead and divide each of these terms, so we're in a plus or minus. So when we first divide one into one and two, that just gives us wanted to when we divide it by 18. So we'd get 1/18 and 2/18 and I know that can simplify, but let's just leave it like that for now. And then we can divide too, so we could get one and for one have and one. Then when we divide by nine, we're going to get won over nine and 2/9. And then when we divide by the re, we will get 1/3 and 2/3 and lastly will divide by six to get 16 and 26 right now to six. We could simplify down to 1/3 uh, to 18th. We can simplify down to one night and don't know. So we have a couple of repeats, so scope through and see which ones we can remove. So one night is repeated so we can get rid of that because it's right here. 1/3 is also repeated cause it's there so we could get rid of that one. And then let's see if there are any other repeats up. We can also get rid of this one here, since we have the one of the very start. But I think that's everything. Now, this is going to make this look a little bit nicer. So we have 121 18 1 huh? One night, to night, 1/3 to third and 16 that these will be all of the possible rational zeros of our function.

Year. Polynomial function affects Quito. Cool times Extra dick are five Linus excuse plus two xy squint plus 12 is given. We have to list for 10 series Nalgae Road. Goodbye. There's no zeros, Totem. You can see that if function it will normal. Function off bigly one and more than one on each positioned. And indeed then be bike. You arresting Eljero off along malfunction. He must be the factor off. Won't stand time off for longer. They must be the fact trough Constanta multiple normal. And you must be the factor off. Leading coefficient off this pull. No get for now, we released all the factors. Both last Well, good to be home. Be equal. Toe last minus one less, minus two. Let's minus three. Best minus four plus minus six and let's minus. But now we released all the factors off Do that. We have to equal toe last minus one and plus minus. So no, we have to find a personal Jiro off dysfunction. So be by sewage rest. Nalgae rode off dysfunction. But now we will find was he will be very cute issues. But this is last minus one by one last minus go buy one blessed minus three by one. Blessed minus for by one and plus minus six by one. Last minus well, by one. And from here, this will be last minus one by two. And this is plus minus two by toe. Already covered. That last minus one by one. And this is plus minus three by two for well, right here. That's minus three by two. This is for where? Two already covered at plus minus two by one. This is six by two. Also cover. And this is well by two so distant. All took over at first. Miners. Six million. Glenn. So this is list off all the potential personal heroes.

The question is even here. Find out the less algae grows after given polynomial. So the polynomial ease off X equal toe, actually power five minus six X s car plus nine x minus tree. So, for finding the messenger goes, we are using the artisanal gelato room, which is scared that the podium is off X called toe. Yeah, after the public. And plus a n minus one, actually problem and minus one. So on digital, then we can like the soldier route as the formal feel like you were. We are the factors off constant. Um, so the constant time is in order. So here we have to find the factors off in order. And you are the factors off leading coefficient off the void, a bills and the leading coefficient off the ball. You know, Mills is in. So here you have to find the factors off here. So for this question, leading coefficient is run and constant coefficient. His ministry. So here the value off we could do this silly plus minus. Well, at blessed ministry que Quito plus minus one. So here the value off be divided like you call to plus minus 1/1 and plus monastery over one. So here the value off feed yard work you called toe plus minus one and blessed ministry. So this is our answer.

Europol Normal function affects people minus six. Time X cubed minus X squared plus X plus 10 is given and we have to list potential Esnal Jiro off this pulling on. So by rest and zeros total we can say that if function it will know mill function off Diggory one for higher than one. We're each coefficient off function. Didn't indeed Er then we can say that people like you. It it is no digital. You must be the vector off course. Tandem off full normal. And you must be the sector off. Leading coefficient off for a moment. For now, we will write all defectors both constant um off normal. So being a quarto Bless minus one last minus two and last minus five. And bless my understand? No, we will write all defectors, both minus six. So feel equal toe last minus one last minus two. Plus my industry when plus minus fixed. You know, we have to find a personal the road, so we will, right B by good issue for people like your issue. Last minus one last minus two plus minus five. Last minus pain. And for two equal to plus minus two. We have plus minus one by two and blessed minus fight by two Last minus two. Bad. We already covered. No, we will right for two. Equal to plus minus three. Then he, by good people toe plus minus one by three, plus minus two by three and plus minus. Bye Bye. Last minus. Penned by three. Now, for Google to plus minus six, we have last minus when by six and plus minus five by six For people to and equal to Plus my understand, it's already covered for Google to plus minus six. So this is a list Both rest nalgae roads off for Norman.


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