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). (12x^2+x−4)÷(3x−2)

Accepted Answer

welcome back. I'm so glad you're here. We get to perform long division. We have our dividend 10 X squared plus three X plus one. All inside the division bracket divided by our divisor which is five x minus one. Alright, how do we do this? Long division will step one in long division is to divide Well maybe maybe more specific. Huh? Okay. What we divide first is the first term in our dividend. So 10 X squared divided by the first term in our divisor. Five X. 10 X squared divided by five X. Is two X. So we're going to write two X above the X term with the same degree in our dividend. Alright, that's step one. Step 2 is to multiply. What are we going to multiply? We're going to take the first term in our quotient up here and multiply it by every term in the divisor. So we'll take two X times five X and that is 10 X squared good. It matches the one right above it. It should then we take two X times a negative one that's minus two X. That is step two. Step three. Is to subtract what are we to subtract? We are going to take the first two terms in our dividend and subtract these two terms in our work down here and 10 X squared minus 10 X squared that zero as it should be. That's great. I'm not going to write zero and I put the parentheses there so that we know we're subtracting both terms, not just the first one and we take three X minus a negative two X which is three X plus two X. So we get five X. That step three step four is to bring down what are we bringing down any relevant terms in the dividend? That will match the number of terms we have in our divisor. So two terms in our work and two terms in the divisor. And then we start back over again with the division. We take the first term in our work down here five X divided by the first term. In our divisor. We take five X divided by five X and five X divided by five X. That's one. So we'll put a plus one here in our quotient. Step two is to multiply will take this one and will multiply it by both terms in the divisor one times five X. Is five x one times negative one is negative one. Next step is to subtract we subtract both the five X and the negative 15 x minus five X. That's nothing one minus negative one. That is the same as one plus one which is two. So if we can't continue with our fourth step, bring down. If there's nothing left to bring down then we're done and whatever we've got down here is a remainder now, how do we write this answer in our proper form? We're going to take our quotient which is two X plus one. And then we're going to add Our remainder which is two, that's going to go in the numerator of a fraction and that will be divided by our divisor, which is five X -1. So this is our answer for our long division. We look at our answer choices in this matches answer choice. A well done. We'll catch you on the next one.

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (12x^2+x−4)÷(3x−2)

Key Concepts

Polynomial Long Division

Quotient and Remainder

Degree of a Polynomial