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ExtGCD : NxN-Nxzxz extGCD(a,0) (a,1,0) . extGCD(a,6) (9,4,$ q X t). if b > 0, where (4,r) divMod(a,b) and (9.s.t) = extGCD(b,r)Problem 5 (3pts) Evaluate extGCD(2...

Question

ExtGCD : NxN-Nxzxz extGCD(a,0) (a,1,0) . extGCD(a,6) (9,4,$ q X t). if b > 0, where (4,r) divMod(a,b) and (9.s.t) = extGCD(b,r)Problem 5 (3pts) Evaluate extGCD(26,91) and verify Bezout $ identity (Please write down the necessary details of your evaluation; YOU don't have t0 write down how YOu evaluate divMod) _

extGCD : NxN-Nxzxz extGCD(a,0) (a,1,0) . extGCD(a,6) (9,4,$ q X t). if b > 0, where (4,r) divMod(a,b) and (9.s.t) = extGCD(b,r) Problem 5 (3pts) Evaluate extGCD(26,91) and verify Bezout $ identity (Please write down the necessary details of your evaluation; YOU don't have t0 write down how YOu evaluate divMod) _



Answers

Given that the identity $f(t)=d(t) \cdot q(t)+R(t)$ holds for the following polynomials, evaluate $f(4)$ $$\begin{aligned} &f(t)=t^{5}-3 t^{4}+2 t^{3}-5 t^{2}+6 t-7 \quad d(t)=t-4\\ &q(t)=t^{4}+t^{3}+6 t^{2}+19 t+82 \quad R(t)=321 \end{aligned}$$

Okay, So this is an interesting application of the, um, definition of the quadratic formula. So we have a quadra X squared, plus B x plus e if we plug in the roots, Um, specifically the one with the plus sign of the minus another word for roots zeros. So this is a zero of this function. So if we plugged that in where you're going to get zero, Thank you very much.

Right. We want to evaluate the given functions. That is H p q equals p minus p minus two Q squared minus five. Few over P plus q. Given h we qualified H and P q plus K. This question is challenging. Or if you have a good multi variant functions in particular is testing our knowledge of the fact that we solved identical to single variable functions. That is we plug in the indicator variables. So for hp Q and we want to find HP Q plus k, we keep the same or wherever we seek you, we replace it with Q plus K. Thus we can proceed to evaluate. So we had HF PQ plus K equals P minus the quantity p minus two times two plus K squared minus five plus K over P plus Q plus K. Factoring out the Q plus k square. The numerator gifts, P minus p minus two Q squared minus four q k minus two K squared minus five to minus five K. All over P plus Q plus k.

This question, given the integral off the one over. Expel P plus one off kill plus x power. I'm the baby off. Kill the X. Now it will send the u he go to the expel one of a que and then did you equal to one of a kill x power off the, uh, minus one. So we have the one minus you dividing by the kill the X. So from here, we can get the X and we go to the gill. And now we got the X power off the thio minus one. Yeah, I'm a que hmm? You on, We can understand. You kill and you power off the Q minus one. Do you? So again, that the X here Now we're ready to replay this integral in terms of the you know, some of the integral I'm the one divided by this one. We can get a culture that you've LP plus one doesn't get equal to that. Uh, you bought the P and the X equal to the kill you about cumin one the u on. Now from here, we can simplify you. Bring the kill outside. Integral on the U boat Q minus one divided by the U boat B plus one Plus you Bell p do you dividing everything by the year Bell p. So we should get equal to the queue in the girl you power off the thio minus one minus p divided by the EU power You last one, do you? And now we can put the the we can go on and on it variable t equal to the new plus one and then d t equal to the d u. And I'm so from here we can get the new equal to the T minus one. Therefore, we can get this integral in terms of the tea now in the car on the T minus one. Power off the, uh K minus one minus b. The running by the tea, the the and from here, we can write this down using the power here. Um, you can get this. Were iko with you that kill and depends on depending on punch. Still, give and be so we can expand this power here using the binomial theorem, and then we can divide invited t. So that's what we think. We will be the form that we can continue here for the channel of value on the Cuban be

So I'm getting to go. This one shows a service truck squared. That makes sense. So I'm gonna make you Could be expelled. Kills gonna be killed. Those eggs. Integrity for that is the you. Because to 10 Q Dick, You fine. Don't you have any cute? So this is what I need. So I'm just gonna do that by time. Do then the big tent together. So So this is in this, and I guess substitute packed. It has been a being one of you trying you 10 on the inter government. That is an end of you of 10. Percy, this thing is me in and out. Keep those Eve's back. 10 c on. We can forget of stricter solution. So it was a church social Certain you worry to be their friendship. Traffic created anxiety. We killed it. Area TV using use insurable. So there is a villain so forced one of 10 where I make understand into Melanie's one of five Q score plus eight. So they were the insert. Refuse. Thank you. Because you're just gonna give me Q Denver for cues. Could close. Aides. She's what I started with so few things, right? You


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