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# Use synthetic division to determine the quotient and remainder.

(x3 − 41x − 30) ÷ (x + 6)

### 2 Answers by Expert Tutors

Michael J. | Effective High School STEM Tutor & CUNY Math Peer LeaderEffective High School STEM Tutor & CUNY ...
5.0 5.0 (5 lesson ratings) (5)
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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
____________________________

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).

Allen E. | Patient and knowledgeble mathematics tutorPatient and knowledgeble mathematics tut...
5.0 5.0 (107 lesson ratings) (107)
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The key value for synthetic division is x + 6 = 0 or x = -6

-6|   1     0    -41    -30
-6    36     30
1   -6     -5    | 0

The bottom line shows the coefficients of the answer with remainder zero

Thus (x3 - 41x - 30)/(x + 6) = x2 - 6x - 5