Divide Using Synthetic Division (3x^2+4x-12)/(x+5)

Problem

(3*x2+4*x−12)/(x+5)

Solution

1. Identify the coefficients of the dividend 3*x2+4*x−12 which are 3 4 and −12

2. Determine the divisor's root by setting x+5=0 which gives x=−5

3. Set up the synthetic division table by placing −5 on the outside and the coefficients 3 4 and −12 in a row.

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

5. Multiply the root −5 by the value in the bottom row 3 to get −15 and place it under the next coefficient 4

6. Add the column values 4 + (-15)t*o*g*e*t11$.

7. Multiply the root −5 by the new value −11 to get 55 and place it under the last coefficient −12

8. Add the final column values −12+55 to get the remainder 43

9. Interpret the resulting values 3 and −11 as the coefficients of the quotient, which is one degree lower than the original polynomial.

Final Answer

(3*x2+4*x−12)/(x+5)=3*x−11+43/(x+5)

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