Use synthetic division and the remainder theorem to find the indicated function value. F(x)=2x^3-6x^2-3x+15, f(-2)
To find the function value of F(x) at x = -2, we can use synthetic division.
First, we set up the synthetic division table using -2 as the divisor:
-2 | 2 -6 -3 15
Next, we bring down the first coefficient, which is 2:
-2 | 2 -6 -3 15
|
|________
2
Next, we multiply the divisor (-2) by the value 2 on the bottom row and write the result (-4) above the next coefficient:
-2 | 2 -6 -3 15
| 4
|________
2 -4
Then, we add this result (-4) to the next coefficient (-6) and write the sum (-10) in the next row:
-2 | 2 -6 -3 15
| 4 -10
|________
2 -4 -10
We continue this process until we reach the last coefficient:
-2 | 2 -6 -3 15
| 4 -10 26
|________
2 -4 -10 41
The last number, 41, represents the remainder of the division.
Therefore, when using synthetic division to divide the function F(x) = 2x^3 - 6x^2 - 3x + 15 by x + 2, the remainder is 41.
As a result, the function value of F(x) at x = -2 is 41.