Divide Using Synthetic Division (-6x^3+2x^2+5x-10)/(x-2)

Problem

(−6*x3+2*x2+5*x−10)/(x−2)

Solution

1. Identify the coefficients of the dividend −6*x3+2*x2+5*x−10 which are −6 2 5 and −10

2. Determine the divisor constant c from the expression x−c Since the divisor is x−2 c=2

3. Set up the synthetic division by placing 2 to the left and the coefficients −6,2,5,−10 in a row.

4. Bring down the first coefficient, −6 to the bottom row.

5. Multiply the divisor 2 by the value just written at the bottom (−6 to get −12 and place it under the next coefficient (2.

6. Add the column: 2 + (-12) = -10$.

7. Multiply the divisor 2 by −10 to get −20 and place it under the next coefficient (5.

8. Add the column: 5 + (-20) = -15$.

9. Multiply the divisor 2 by −15 to get −30 and place it under the last coefficient (−10.

10. Add the final column: −10+(−30)=−40 This is the remainder.

11. Interpret the resulting coefficients −6,−10,−15 as the coefficients of the quotient polynomial, which will be one degree lower than the original.

Final Answer

(−6*x3+2*x2+5*x−10)/(x−2)=−6*x2−10*x−15−40/(x−2)

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