In Exercises 17–32, divide using synthetic division. (2x^2+x−10)÷...

Question

In Exercises 17–32, divide using synthetic division. (2x^2+x−10)÷(x−2)

Accepted Answer

Hey everyone here we are asked to use synthetic division to find the quotient of the quantity of four X squared minus X minus 64 divided by the quantity of x minus eight. Now to solve this with synthetic division, we set up a division like four format where we have all the coefficients on the right hand side. So starting with the highest power of X, we have X squared and its coefficient is four. We then move on to X to the power of one which has a coefficient of negative 24. Then we move on to X to the power of zero which Has a coefficient of -64. And next we have to find the number the constant for the left hand side. So all we have to do is take the opposite sign of the constant in the divisor which in this case is the opposite of -8 which gives us positive eight. So to start solving we first just bring down the first coefficient here which is four. Without making any changes. We then bring four to the next column and multiply it by the constant, which is eight. So we have four times eight which gives us 32. We then add these two coefficients together. So negative 24 plus 32 gives us positive eight. We then repeat the process. Now taking the eight times the constant eight which gives us positive 60 for adding the two coefficients together we have 64 plus negative 64 which just gives us zero. So next we see that we have all of our coefficients and all of the coefficients, aside from the last one are coefficients of the quotient, but this last coefficient here is the remainder. So we see that the remainder is equal to zero. Next with these coefficients, they all match up with the following X to whichever power. So our final solution here, the quotient is four X plus eight with a remainder of zero. And this is our answer here for choice. B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 17–32, divide using synthetic division. (2x^2+x−10)÷(x−2)

Key Concepts

Synthetic Division

Polynomial Functions

Remainder Theorem