Divide Using Synthetic Division (16x^3+80x^2+x+5)/(x+5)

Problem

(16*x3+80*x2+x+5)/(x+5)

Solution

1. Identify the divisor and the root. The divisor is x+5 which corresponds to a root of k=−5

2. List the coefficients of the dividend 16*x3+80*x2+x+5 The coefficients are 16 80 1 and 5

3. Set up the synthetic division table by placing the root −5 to the left and the coefficients in a row.

4. Bring down the first coefficient, 16 to the bottom row.

5. Multiply the root −5 by the value in the bottom row 16 to get −80 and place it under the next coefficient 80

6. Add the column: 80 + (-80) = 0$.

7. Multiply the root −5 by the new value 0 to get 0 and place it under the next coefficient 1

8. Add the column: 1 + 0 = 1$.

9. Multiply the root −5 by the new value 1 to get −5 and place it under the last coefficient 5

10. Add the final column: 5 + (-5) = 0$. This is the remainder.

11. Interpret the resulting coefficients 16 0 and 1 as the coefficients of a polynomial with a degree one less than the original.

Final Answer

(16*x3+80*x2+x+5)/(x+5)=16*x2+1

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