To determine whether the above expression is divisible by (x + 5), we can use synthetic division. To do that, we'll remove the variables in the expression and just used the numerical coefficients.
Also, the divisor (x + 5) will now become -5. See the illustration below.
The next thing to do is to bring down the first coefficient that is -5 then multiply this to the divisor. The answer will be written under the second coefficient. (-5 x -5 = 25) Then, add the answer to the second coefficient. (-29 + 25 = -4)
Do the same process all through out until the last column.
-4 will now then be multiplied to -5 and the answer 20 will be added to -17. Then, -17 + 20 = 3.
3 times -5 = -15. 15 + (-15) = 0
We have finished dividing the expression using synthetic division. The quotient is -5x² - 4x + 3.
As you can see in the table, the last column ends in zero, hence, there is no remainder for this division.
Hence, (x + 5) is a factor of (-5x³ -29x² - 17x + 15).