We DO use synthetic division for problems like #2. There are a couple processes that can be used. PLEASE don't just change a problem and act like that's OK.

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The purpose he was pointing out is when you use Synthetic Division you have to find the zero, or root of a polynomial in the denominator. For the case of: [ x - 1 ], if we let this term equal to zero then the variable X must be a positive one to make it equal to zero. If we you can't do this operation then you have to use long division.