Divide Using Synthetic Division (5x^3+18x^2+7x-6)/(x+3)

Problem

(5*x3+18*x2+7*x−6)/(x+3)

Solution

1. Identify the root of the divisor by setting x+3=0 which gives x=−3

2. Set up the synthetic division by listing the coefficients of the dividend: 5 18 7 and −6

3. Bring down the first coefficient, 5 to the bottom row.

4. Multiply the root −3 by the value in the bottom row (5 to get −15 and write this under the next coefficient (18.

5. Add the values in the second column: 18 + (-15) = 3$.

6. Multiply the root −3 by the new value (3 to get −9 and write this under the next coefficient (7.

7. Add the values in the third column: 7 + (-9) = -2$.

8. Multiply the root −3 by the new value (−2 to get 6 and write this under the last coefficient (−6.

9. Add the values in the final column: −6+6=0

10. Interpret the resulting coefficients 5 3 and −2 as the coefficients of a polynomial one degree lower than the original, with the final 0 as the remainder.

Final Answer

(5*x3+18*x2+7*x−6)/(x+3)=5*x2+3*x−2

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