Let's do one more syntheticdivision example. And in anothervideo, we actually have actually the why this functions relativeto algebraic long division. However here it's goingto be one more just, let's go throughthe procedure of it just so that you getcomfortable with it. And also now is a good chance togive it a shot, come actually shot to leveling thisrational expression. Therefore let's think aboutthis step by step. For this reason the very first thingI desire to perform is write every one of the coefficientsof the numerator. Therefore I have actually a 2. Oh, I have to be cautious here. Because the 2 is thecoefficient for x come the fifth, I have actually no x to the 4th term. Allow me begin over. So I have actually the 2 from2x come the fifth. And then I have nox come the fourth. So it's yes, really 0x come the fourth. Therefore I'll placed a 0as the coefficient for the x come the 4th term. And then I have a negative1 time x come the third. And then I have a positive3 time x squared. An adverse 2 times x. And then I have a constantterm, or zero degree term, the 7. Ns just have actually a confident 7. And now let me just attract mylittle funky synthetic department operator-looking symbol. And remember, the type ofsynthetic department we're doing, the only applies when us aredividing by an x to add or minus something. There's a slightlydifferent process you would need to do if itwas 3x or if was an unfavorable 1x or if it to be 5x squared. This only works once we havex plus or minus something. In this case we have actually x minus 3. Therefore we have the negative 3 here. And the processwe show-- there's other ways of law it-- isyou take it the an unfavorable of this. So the an unfavorable ofnegative 3 is optimistic 3. And also now we're prepared to performour artificial division. For this reason we'll carry downthis 2 and then multiply the 2 time the 3. 2 time 3 gives us 6. 0 plus 6 is 6. And also then us multiply the timesthe 3, and also we gain positive 18. An adverse 1 to add 18 is 17. Multiply the times the 3. 17 time 3 is 51. 3 to add 51 is 54. Multiply the times 3. The numbers are gettingkind of huge now. Therefore that's going to be what? 50 times 3 is 150. 4 times 3 is 12. For this reason this is walk to be 162. Negative 2 add to 162 is 160. And also then finally, 160times 3 is walking to be 480. And also you add 480 to7, and you acquire 487. And also you can think the it, i onlyhave one ax or one number to the left-hand sideof this bar here. Or I'm simply doing the standard,traditional x plus or minus something version of syntheticdivision, I have to say. Therefore I can separatethis out, and now I've essentially gotten my answer. And also it looks like voodoo,and it type of is voodoo. And that's why Idon't choose to execute it, because you're justmemorizing an algorithm. But there space othervideos why we explain why. And also it can be fastand convenient and document saving an extremely often,like friend see best here. But then us haveour last answer. It's going come be-- andlet me work-related backwards. Therefore I'll start withour remainder. Therefore our remainder is 487. And it's going come be487 end x minus 3. And so this isour continuous term. And so you're going to have plus160 add to 487 end x minus 3. Currently this is our x term. For this reason it's going to be54x plus all of this. This is going to beour x squared term. For this reason this is walking to be 17xsquared to add 54x plus 160 and all of that. Climate this is walking tobe x to the 3rd term. Therefore this is walk to it is in 6x tothe 3rd plus all of that. And also then finally, this isour x come the 4th term-- 2x to the fourth. And let me erase this. So climate I have actually my xto the 4th term. So it is 2x come the fourth. And we are done.

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This thing simplifiesto this appropriate over here. And also I encourage you come verify itwith timeless algebraic long division.