Use synthetic division and the remainder theorem to find P(a).
P(x)=x^3+3x^2-7x+7; a=4
To find P(a), where P(x) = x^3 + 3x^2 - 7x + 7 and a = 4, we can use synthetic division.
First, set up the synthetic division with the coefficients of P(x) and the value of a:
4 | 1 3 -7 7
Next, bring down the first coefficient:
| 1
Multiply a by the first coefficient and write the result under the next coefficient:
| 1
------
| 4
Add the two numbers in the second column:
| 1
------
| 4 7
Multiply a by the new number and write the result under the next coefficient:
| 1 4
------
| 4 7
Add the two numbers in the second column:
| 1 4
------
| 4 11
Multiply a by the new number and write the result under the next coefficient:
| 1 4 -3
------
| 4 11
Add the two numbers in the second column:
| 1 4 -3
------
| 4 8
The remainder is the last number in the second column, which is 8. Therefore, P(4) = 8.