Answer:
578
Explanation:
By the remainder theorem, if a polynomial, f(x) is divided by a linear factor x-a, then the remainder of the division is f(a).
[tex]f(x)=3x^5-4x^3-5x^2+2[/tex]
To determine f(3) using synthetic division, we find the remainder when f(x) is divided by x-3. i.e.
[tex]\frac{3x^5-4x^3-5x^2+2}{x-3}[/tex]
The synthetic division table is attached below:
Therefore, the value of f(3) is 578.
