5

(b) (10 points)2)'+ ()"+ (9)"...

Question

(b) (10 points)2)'+ ()"+ (9)"

(b) (10 points) 2)'+ ()"+ (9)"



Answers

Add. $$\frac{7}{b}+\frac{9}{b}$$

Okay for this question were being asked to multiply negative B times B plus nine. In order to do that, we're gonna use distribution. So we'll start by distributing to the first term. So that's gonna be negative B times B. For the first distribution. And then we'll distribute to the second term. So we'll have negative B times positive nine. Yeah. So now we just need to simplify that for our first term negative B times B, we can write that as negative B squared. And then for the second term it's a negative. So we'll put a minus in between and then for B. Times nine um it's most proper to write that with the number in front. So we're going to write that as nine B. So our product on this question is negative B squared minus nine B.

So we have to be over. B plus nine equals. I'm sorry. Minus 58 Bulls three over. V plus. None. Since the common denominator is B plus nine. And we just need to multiply five by that. So we get to be monos pop toms B plus non equals three. And so to be monos Bobby minus 45 equals three negative three b then well, he will where you live. I'm sorry. Big One for 48 I can't add today and then dividing gives us be equal to negative 16.

Okay, so we have a big on line plus six. So that's the six Samos six minutes line, which is equal to negative three, which is, um

So when we're trying to simplify both of these Poland, no meals were going to set it up as in long division format. Now, when we're trying to simplify any of these polynomial is when they're getting divided by each other, there are many different methods. You could do such a synthetic division and other different types of methods, but in this case, Long division works the best. So now that we got this set up, we know in the end this whole thing, when we're subtracting by the different things, the remainder in the end needs to come to zero. So that's our goal. So once we get the remainder to be zero, we know that the answer on the top is the right answer. That's what happens when we divide both. The polynomial is by each other. Now that we kind of established that back, we're going to figure out how to go about the snow. So first, we're going to try to get this term to be zero. So to do that, we're gonna we're gonna get three, be at the top, and we're going to do three b times the polynomial three B minus two in doing that? Weekend nine B squared minus six B. And they were going to subtract both of these, and we're gonna get canceled. Also. Just become zero, and then we have plus 15 beat minus 10 you. Now that we got that, we're going to try to get this whole thing to be cereal. In order to do that, we're gonna get plus five appears so five times a polynomial three B minus two. When we do that, we're going to get that down here, and we're going to get 15 B minus 10. And that means that we subtracted. This just cancels out. So we get zero here, and that means our remainder is zero. So, yeah, we've reached our final goal. So that means this answer at the top is what happens when we divide this polynomial by this polynomial. So again, our final answer is three B plus five


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