Did you know you could do this division using the approach "synthetic division?"
The coefficients of the dividend x^2 - 2x - 48 are 1, -2 and -48. The divisor x+5 yields the divisor -5 for use in synthetic division. Proceeding with the synthetic div.:
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-5 / 1 -2 -48
-5 35
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1 -7 -13
Thus, the quotient is 1x - 7 with a remainder of -13. This also means that if we substitute -5 for x in the original function, the result will be -13.