(x3 − 41x − 30) ÷ (x + 6)
The process is the divide the coefficients (descending order of variable) of the dividend by the possible root (divisor).
Since -6 is your possible root, we set up the division as this.
-6 | 1 0 -41 -30
-6 36 30
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1 -6 -5 0
As you can see, the digits below the line is the quotient. The last digit under the line is the remainder.
Quotient = x2 - 6x - 5
Remainder = 0
If the reminder is zero, then the quotient is a factor of the dividend. In this case, we have a remainder of zero. Therefore,
(x2 - 6x - 5) is a factor of (x3 - 41x - 30).