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). (3x^2−2x+5)/(x−3)

Accepted Answer

hey everyone here are asked to find the quotient of the expression using long division. So setting this up in long division formatting on the right hand side we need our dividend which is four x squared minus three X plus eight. And on the left hand side we need our divisor which is x minus one. Now to solve this we begin by taking the leading term of the dividend and dividing it by the leading term of our divisor. So we have four X squared divided by X. Which if you recall the product rule for exponents as well as the rule for negative exponents. This expression here simplifies to four X. We then take this term and add it to the top of the bar. So four X becomes our first term of the quotient. And then from here we take this term and multiply it by our divisor. So we have four x times the quantity of x minus one. Multiplying. We get four x squared minus four X. We then take this result and subtract it from our dividend. So subtracting, we have minus the quantity of four X squared minus four X. And now we can see that the x squares cancel. So we get zero, we then have negative three X minus negative four X giving us positive X. We then bring down our last term here which is just plus eight. We then repeat this process, taking the leading term of our remainder and dividing it by the leading term of the device. So we have x divided by X which is simply equal to one. We then take one and add it to the top of the bar. So positive one becomes the second term of our quotient. We then take one and multiply it by our divisor. So we have one times the quantity of X -1 which is simply equal to X -1. We then take this result and subtract it from our remainder. So we have minus the quantity of x minus one. Subtracting. We see that the X's cancel and give us zero. We then have eight minus negative one which gives us positive nine and now remainder is less than the degree of the divisor. So we are done with this process and we see that we have a remainder of nine. Now with this our quotient is simply four X plus one plus nine divided by the quantity of x minus one which is our answer here for choice. D Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (3x^2−2x+5)/(x−3)

Key Concepts

Polynomial Long Division

Quotient and Remainder

Degree of a Polynomial