Use synthetic division to find P(3) for P (3) = x* - 6x3 - 4x2 - 6x - 2
To find P(3), we can use synthetic division.
The coefficients of the polynomial are: -6, -4, -6, -2, and we write them out in a long division format:
3 | -6 -4 -6 -2
|_________
|
First, bring down the coefficient of the highest power of x, which is -6:
3 | -6 -4 -6 -2
|_________
| -6
Next, we multiply the divisor (3) by the result at the bottom (which is -6), and place the result below the next coefficient:
3 | -6 -4 -6 -2
|_________
| -6
| -18
We continue this process for each coefficient:
3 | -6 -4 -6 -2
|_________
| -6
| -18 -54
|_____________
0 -4
The last number at the bottom, which is -4, is the remainder.
Therefore, P(3) is equal to the remainder, which is -4.