Divide Using Synthetic Division (2x^3-2x^2+x-1)/(x-3)

Problem

(2*x^3−2*x^2+x−1)/(x−3)

Solution

1. Identify the coefficients of the dividend 2*x^3−2*x^2+x−1 which are $2, -2, 1, -1,a*n*d(t)*h*e*z*e*r*o*o*ƒ*t*h*e*d(i)*v*i*s(o)*r - 3,w*h*i*c*h*i*s() = 3$.

2. Set up the synthetic division by writing the zero 3 to the left and the coefficients in a row.

3. Bring down the first coefficient 2 to the bottom row.

4. Multiply the zero 3 by the value just written in the bottom row 2 to get 6 and place this under the next coefficient −2

5. Add the column values −2+6 to get 4 and write this in the bottom row.

6. Multiply the zero 3 by the new value 4 to get 12 and place this under the next coefficient 1

7. Add the column values $1 + 12t*o*g*e*t3$, and write this in the bottom row.

8. Multiply the zero 3 by the new value 13 to get 39 and place this under the last coefficient −1

9. Add the final column values −1+39 to get the remainder 38

10. Interpret the resulting coefficients $2, 4, 13$ as the coefficients of the quotient polynomial, which will be one degree lower than the original.

Final Answer

(2*x^3−2*x^2+x−1)/(x−3)=2*x^2+4*x+13+38/(x−3)

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