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Eist all i& zetcs offfr) = Zx S-,+ by iesting the possible raticnal Zet Iiseeii#3_ Dxpcrt your answer by showing synthetic division...

Question

Eist all i& zetcs offfr) = Zx S-,+ by iesting the possible raticnal Zet Iiseeii#3_ Dxpcrt your answer by showing synthetic division

Eist all i& zetcs offfr) = Zx S-,+ by iesting the possible raticnal Zet Iiseeii#3_ Dxpcrt your answer by showing synthetic division



Answers

Divide by using synthetic division. Check your answer by multiplication. $$\left(2 z-2 z^{2}+z^{3}-5\right) \div(z+3)$$

Oh, you're doing well. So in order to divide these two expressions here, using synthetic division, need to write out all the coefficients of this first expressions. This is a coefficient of one in front of the execute. So the coefficients are wine. Seven 13 in six. And then for this X plus two, we rewrite this in the form X minus K will be X minus. Minus two K is equal to minus two. That means we're going to put minus two on the outside here. So then dividing this, you can bring this one down. This first term. Down here, it's multiplying. One by minus to get minus 27 Minus shoes. Five, five times minus two. You is minus 10 13 minutes. Sentence 33 times minus use minus 66 minus 60 So this is zero. Here. This last term is our remainder. Since it's a remainder of zero, we don't have any. Remain. So we've got a first term ist one. That's one X squared plus five eggs plus three. This is our final. It's right here. This is a result of this synthetic division for this problem. All right, Well, thanks. And I hope that hoped

This question asked is thes synthetic division to divide these two expressions and we happen Double check two things before you can begin first is that our dividend, which is the first set of parentheses, is in decreasing exponential order, which we see because we have 32 10 for exponents. And the second thing is our divisor is in the form Z minus C, which it is. And we just have to remember that we take the opposite sign of this number here when we do the division. So in this case, it's a positive three. And now we're going to take the coefficients. Ah, each term in our dividend. So we have four minus 11 minus six and 10. And when we do synthetic division, we always just bring down this first term. So we have a four in this case, and now we take four and we're going to multiply it by this three here and that gives us 12 Oro me, right this in a different color 12. And now you always just on the numbers in the column. So we have a minus 11 plus a positive 12 which just gives us one and Now we're going to take one, and we're going to multiply it by the free, which just gives us three. And again we're going to add the numbers in the column. So minus three plus a positive three gives us e negative three. And now we'll take negative three and multiply it by this three, which gives us negative nine. And now we have 10 plus negative nine, which gives us one as a remainder. And when we have a remainder, when we do this type of division, we have to ray a fraction. Where are numerator is the remainder and our denominator is the divisor. So that means we get a final answer of or Z squared plus C minus three plus one, and our divisor is Z minus three.

Hope you're doing well. So in order to divide these two expressions using synthetic division, you first need to write out all of the coefficients of this new. The first you may notice that there is no X to the fifth term. It was extra sixth and skip sex in the fourth and 3rd 2nd It's Sarah that there's no exit of this. We used to remember Write that in. It's plus zero x to the pit. We need to include this coefficient here in our synthetic division. So writing out old are coefficients for the numerator. We have one here, right With six. We have to conclude this is zero for excellently. We've got minus three. Got to We have minus six. We have minus five. Then we've got three. The now for this X plus two term here. Need to write this in the form X minus kitty, that's going to equal to X minus minus two, which is the same as expose to where K is equal to minus two. We're gonna put minus two here on the outside and then using synthetic division to divide this. You can bring this one down. We've got one times minus two gives us minus 20 Minus two is minus two when it's two times minus two. Gives us four minus three plus four. Gives this one one times minus two. Is this minus two to minus 20 Dear. Attempt minus two gives us zero minus six plus zero. Just minus six, then minus six times minus two. Gives us 12 minus five plus 12 Gives us seven, then seven times minus two. Is this minus 14? Three minus 14 is minus 11. So this right here is our next term. Uh, this right here is gonna hear. Excellent. Fourth, this is our ex Cubes term. This is our X squared turn. It's our X to the first. True, this is their X zero turn or just are constant and that our last term will always be our remainder her. So then writing out our final Ansari of one times x it if if that's exited bit minus two x to the fourth. What's one excuse that just plus excuse This is your ex squares. We don't have to write that in minus six. Acts there that are constant is plus seven. We have a remainder of minus 11 out of our full. Our denominator for this division is X plus juice. Remainder is going through minus 11. Overexpose to We're just gonna add that onto the end here. So that's minus 11. Over X plus two. This is our final answer right here. This is a result of synthetic division for this problem. All right, Well, thanks. And I hope that helps.

Hello. I hope you're doing well. So in order to vote to divide thes two expressions using synthetic division first each write out all of the coefficients of this First this the expression in the numerator So are coefficients are going to be wine re to you to three and one and then for a denominator, we've got X plus twos. We need to rewrite this in the form X minus K. So it's going to be X minus minus two, which is the same as X Plus two, in which Case K is equal to minus two. We're gonna get a pump minus two on the outside. Here it's now we're going to use synthetic to division to divide this. We can bring this one down about one times minus two gives us minus 23 minus two. Use one one times minus two again gives us minus two to minus 20 zero times minus 202 plus year was to do you times lettuce to his minus for three minus four is minus one minus one times minus two. Gives us two on one plus two is three. So in terms here, this is our extra fourth term. This is our executed stream. This is our X squared term is our ex term. This is our X zero term or just are constant then this here is our remainder. So writing this out then if one x to the fourth it was one x cubed zero X squared is we don't have to write that out was two acts There are constant is just minus one. Then we have a remainder of re. And this this three are denominator here was explicit. Oops. That means our remainder is going to be three over X plus two. This is plus three over X plus two. His three is our remainder and x plus twos are total amount that we're dividing. So this is our final answer right here. This is a result of synthetic division for this problem. All right, Well, thanks. And I hope that hoped


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