Divide Using Synthetic Division (6x^5-5x^4+x-4)/(x+1/2)

Problem

(6*x5−5*x4+x−4)/(x+1/2)

Solution

1. Identify the divisor and the root. The divisor is x+1/2 so the root used for synthetic division is r=−1/2

2. List the coefficients of the dividend 6*x5−5*x4+0*x3+0*x2+1*x−4 Ensure that zeros are included for the missing x3 and x2 terms: 6, -5, 0, 0, 1, -4$.

3. Set up the synthetic division table by bringing down the first coefficient, 6

4. Multiply the root −1/2 by the value just written below the line (6 to get −3 and place it under the next coefficient (−5.

5. Add the column: −5+(−3)=−8

6. Repeat the multiply-and-add process for the remaining coefficients:

• −1/2×(−8)=4⇒0+4=4

• −1/2×4=−2⇒0+(−2)=−2

• −1/2×(−2)=1⇒1+1=2

• −1/2×2=−1⇒−4+(−1)=−5

7. Interpret the resulting row 6, -8, 4, -2, 2, -5$. The first five numbers are the coefficients of the quotient polynomial (one degree lower than the dividend), and the last number is the remainder.

Final Answer

(6*x5−5*x4+x−4)/(x+1/2)=6*x4−8*x3+4*x2−2*x+2−5/(x+1/2)

Want more problems? Check here!