Use synthetic division to find P(-2) for P(x)=x^4-5x^3+3x+2 show your work
To find P(-2), we substitute -2 into the polynomial P(x) and perform synthetic division.
First, set up the tabular form of synthetic division:
| 1 | -5 | 3 | 0 | 2
-2 |
Bring down the coefficient of the highest power term, which is 1:
| 1 | -5 | 3 | 0 | 2
-2 | 1
Multiply -2 by 1 and write the result under the next coefficient, -2 multiplied by -2:
| 1 | -5 | 3 | 0 | 2
-2 | 1 | -2
Add the numbers vertically: -5 + (-2) = -7:
| 1 | -5 | 3 | 0 | 2
-2 | 1 | -2
-7
Multiply -2 by -7 and write the result under the next coefficient, -2 multiplied by -7:
| 1 | -5 | 3 | 0 | 2
-2 | 1 | -2 | 14
Add the numbers vertically: 3 + 14 = 17:
| 1 | -5 | 3 | 0 | 2
-2 | 1 | -2 | 14
-7 | 17
Multiply -2 by 17 and write the result under the next coefficient, -2 multiplied by 17:
| 1 | -5 | 3 | 0 | 2
-2 | 1 | -2 | 14 | -34
Add the numbers vertically: 0 + (-34) = -34:
| 1 | -5 | 3 | 0 | 2
-2 | 1 | -2 | 14 | -34
-7 | 17 | -34
Multiply -2 by -34 and write the result under the next coefficient, -2 multiplied by -34:
| 1 | -5 | 3 | 0 | 2
-2 | 1 | -2 | 14 | -34 | 68
Add the numbers vertically: 2 + 68 = 70:
| 1 | -5 | 3 | 0 | 2
-2 | 1 | -2 | 14 | -34 | 68
-7 | 17 | -34 | 70
The remainder is 70.
Therefore, P(-2) = 70.