Final answer:
Synthetic division is a method used to divide polynomials. In this case, we evaluate f(x) = 4x³ - 10x² + 3x - 5 at x = 2 using synthetic division, resulting in a remainder of -8.
Step-by-step explanation:
Synthetic division is a method used to divide polynomials. In this case, we have the polynomial f(x) = 4x³ - 10x² + 3x - 5 and we want to evaluate it at x = 2, which is represented by f(2). Synthetic division allows us to simplify the division process and find the remainder.
To perform synthetic division, we divide the coefficients of the polynomial by the value of x - 2, since we are evaluating at x = 2. Writing the coefficients in descending order, we have 4, -10, 3, -5. Performing the synthetic division gives us a remainder of -8:
4 | -10 3 -5
|
| -32 14 -2
|
| 2 6 -8
Therefore, when f(x) = 4x³ - 10x² + 3x - 5 is evaluated at x = 2, the result is a remainder of -8.