Divide using synthetic division: 2a^3+7a^2-a-2 by 2a+1

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There is a way to use synthetic division to divide by a factor of the form ax+b and not x+b. That method requires an addition of a line at the end of the problem.

The best way to work out the given problem is to use regular long division.

`a^2+3a-2`

2a+1 `2a^3+7a^2-a-2`

`2a^3+a^2`

`6a^2-a`

`6a^2+3a`

`-4a-2`

`-4a-2`

0

Hence the answer is `a^2+3a-2`

I included a link to a blog that shows you how to perform long division if the leading coeficient of the divisor is not 1.

**Sources:**

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