Is x + 10 a factor of the function f (x) = x^3 - 75x + 250?

We can use synthetic division as a short cut solution to answer this problem. First is we put the root on the left side and the numerical coeff. in the right side.  Then we bring down 1 and start multiplying to the root. Add the numbers in column.

-10 | 1   0   -75    250 
           -10   100  -250
        1 -10    25     0
Since the final answer is 0, x + 10 a factor of the function f (x) = x^3 - 75x + 250.

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