Use either long division or synthetic division to divide

Question

5x³⁺x²-3x+7 by x-1

Answer 1

Synthetic is easier.

1   |   5   1   -3   7

              5    6   3

         5   6    3   10

Thus:  5x^2  +  6x   +  3  +  10/(x-1)

Answer 2

I'll guide you through the long division method. It does help if you remember how to do long division of integers.

Start by trying to divide x-1 into 5x³+x². Focus on what you would need to multiply x by to get 5x³. If you multiply  x by 5x² you get 5x³, so let's try (x-1)(5x²) which gives 5x³-5x².

Write 5x³-5x² directly underneath 5x³+x² and subtact. You get 6x² because x²-(-5x²) = 6x²

So the first term in your answer is 5x² and you have a remainder of 6x². Bring down the next term in your dividend, which is -3x. Add it to your remainder and start again.

This time you are dividing x-1 into 6x²-3x. Focus on the x and the 6x. Keep doing this same process until you have brought everything down and divided. You will either have no remainder at the end, which means it divided evenly, or you will have something left. If there is a remainder, take that expression and divide it by x-1, your divisor. That fraction is added on to the end of your quotient.