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Let's try one:

( x^2 - 9 ) / ( x + 7 )

Set it up and remember the dummy guy:

( x^2 + 0x - 9 ) / ( x + 7 )

Start working it...

dividing gives x as the first term of the answer ... multiplying to ( x + 7 ) gives ( x^2 + 7x ) ... subtracting gives -7x


after bringing down the -9, dividing gives -7, multiplying to ( x + 7 ) gives ( -7x - 49 ) ... subtracting gives 40 ... x does not go into 40

40/x does NOT reduce!

So, we stop here and the 40 is our remainder.

Here's the official answer:

( x^2 - 9 ) / ( x + 7 ) = x - 7 + ( 40 / ( x + 7 ) ) ... x + 7 is the original divisor


TRY IT:

( x^3 - 2x^2 + x - 6 ) / ( x - 3 )