5x^{3+}x^{2}-3x+7 by x-1

Synthetic is easier.

1 | 5 1 -3 7

5 6 3

5 6 3 10

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

5x^{3+}x^{2}-3x+7 by x-1

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Synthetic is easier.

1 | 5 1 -3 7

5 6 3

5 6 3 10

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

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 5x^{3}+x^{2}. Focus on what you would need to multiply x by to get 5x^{3}. If you multiply x by 5x^{2} you get 5x^{3}, so let's try (x-1)(5x^{2}) which gives 5x^{3}-5x^{2}.

Write 5x^{3}-5x^{2} directly underneath 5x^{3}+x^{2} and subtact. You get 6x^{2} because x^{2}-(-5x^{2}) = 6x^{2}

So the first term in your answer is 5x^{2} and you have a remainder of 6x^{2}. 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 6x^{2}-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.