Divide Using Synthetic Division (5x^3+6x+8)/(x+2)

Problem

(5*x3+6*x+8)/(x+2)

Solution

1. Identify the coefficients of the dividend 5*x3+0*x2+6*x+8 Note that a 0 is used for the missing x2 term.

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

3. Set up the synthetic division table by placing −2 to the left and the coefficients 5, 0, 6, 8$ in a row.

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

5. Multiply the divisor −2 by the value in the bottom row 5 to get −10 and place it under the next coefficient 0

6. Add the column values: 0 + (-10) = -10$.

7. Multiply −2 by −10 to get 20 and place it under the next coefficient 6

8. Add the column values: 6 + 20 = 26$.

9. Multiply −2 by 26 to get −52 and place it under the final coefficient 8

10. Add the column values: 8 + (-52) = -44$. This last value is the remainder.

11. Interpret the resulting coefficients 5, -10, 26a*s(t)*h*e*q*u*o*t*i*e*n*tx^2 - 10x + 26w*i*t*h*a*r*e*m*a*i*n*d(e)*r*o*ƒ44$.

Final Answer

(5*x3+6*x+8)/(x+2)=5*x2−10*x+26−44/(x+2)

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