In Exercises 1–16, divide using long division. State the quotient...

Question

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (2x^3+7x^2+9x−20)/(x+3)

Accepted Answer

Welcome back. I'm so glad you're here. We get to perform long division. Our dividend which goes inside the division bracket is three X cubed plus 31 X squared plus 43 X plus division bracket that's divided by our divisor which is X plus nine. And how do we do long division? Well, step one is going to be divide. Well what do we divide? We're going to take the first term of our dividend divided by the first term of our divisor. So three X cubed divided by X and three X cubed divided by X is three X squared. I'm going to put that up here above the X squared in our dividend So that they line up step two in Long Division is to multiply, what do we multiply? We take the first term of our quotient and we're going to multiply it by each term in our divisor from left to right. So in this case we'll start off with three X squared times X. Three X squared times X is three X cubed and this is great. If it matches the term right above it then we've done it correctly. Then we take three X squared times nine. So that's going to be plus 27 X squared. Step three for Long Division is to subtract what do we subtract? We subtract the relevant terms in our dividend by the terms that we just created below it. I put a parentheses there so that we know we're subtracting both of those terms and not just the first term. So three X cubed minus three X cubed is nothing. I'm not going to write zero but there's a zero and 31 X squared minus 27 X squared is four X squared Step four in long division is to bring down what are we going to bring down? We bring down the next relevant term from our dividend. So we'll bring down this plus 43 X. So that we've got matching number of terms that we're working with in our work space here as the divisor. Now we start over again, we ask ourselves this first term in our work here for X squared divided by X four X squared divided by X is going to be plus four X. Now we go to step two to multiply, we're going to multiply our four x times both terms and our divisor four X times X is for X squared great. That matches the one above it and for X times nine is plus 36 X. Step three. We divide or excuse me, we subtract four X squared minus four X squared is nothing great. 43 X minus 36 X is going to be seven x. Step four is to bring down, we'll bring down plus 58 we resume with step one again. We ask ourselves this first term in our work here divided by the first term in our divisor. So we have seven X divided by X and seven X divided by X is plus seven. Next we are going to multiply so we'll take our new term in the quotient seven times both terms in our divisor. Seven times X is seven X. Good. That matches the one above it. Seven times nine is plus 63. Step three to subtract seven X minus seven X is nothing great. 58 -63 is a negative five. Now, if there's nothing left to bring down, that's as far as we can go. So we stop here and what we've got down here is our remainder. Now how do we write this in the proper form? We are going to take our quotient. So that's up in red. We've got three X squared plus four X plus seven and then we're going to add our remainder which is going to go in the numerator. So our remainder is negative. Five over are divisor. That was X plus nine and that is our answer to our long division. We look at our answer choices and this matches with answer choice C. Well done. We'll catch you on the next one

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In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (2x^3+7x^2+9x−20)/(x+3)