Question

How do you divide `(3x^3+4x^2+x+1)÷(x-1)`?

Answer 1

`3x^2+7x+8+(9)/(x-1)`

Explanation:

You can use Remainder Theorem or Synthetic Division to do so. I will use the Synthetic Division since it is quicker and easier (but it only works for a polynomial divided by a binomial).

The first step in using theSynthetic Division is to find out what makes the binomial `0`. In this case, it is `1`. Now, you put that number in a sort of secluded area like so:

`1" "|`

Then, you determine the co-efficients for every term in your polynomial (you MUST also include co-efficients of `0`. However, there are none in this problem). Then, you make a list like this:

`1" "|color(white)(xx)3" " "4" " "1color(white)(xx)1`

Then, you do this little trick where you bring down the first number (`3`), multiply by the secluded number (`1`), put the answer down under the next number (`4`), and then add. After its all done, it'll look like this:

`1" "|color(white)(xx)3" " "4" " "1color(white)(xx)1`
`color(white)(xxxxxx)darrcolor(white)(x)3" " "7color(white)(xx)8`
`color(white)(xxxxx)stackrel("---------------------------------")`
`color(white)(xxxxxx)3" " "7" " "8|color(white)(x)9`

Now, the remainder has the co-efficients on the third line (`3`, `7`, and `8`), making the polynomial `3x^2+7x+8`. The `9` is the remainder (divided by the binomial).

All-in-all, the answer is:

`3x^2+7x+8+(9)/(x-1)`.

I know the description was confusing, which is why I have attached a link to a video that will do a better job explaining it to you!