Use synthetic division and the remainder theorem to find P(a).
P(x)=x^3_5x^2-6x+4; a=3
To use synthetic division, we will first set up the divisor as (x - a), where a = 3. So the divisor is (x - 3).
The coefficients of P(x) are 1, -5, -6, and 4. We will use synthetic division with the coefficients and the divisor.
The synthetic division process is as follows:
3 | 1 -5 -6 4
| 3 -6 0
--------------------
1 -2 -6 4
The last number on the bottom row, 4, is the remainder when P(x) is divided by (x - 3). Therefore, P(3) = 4.
Hence, P(3) = 4.