The value of f(-3) in the given function is 144.
Division of polynomial function.
The division of a polynomial function can be done by using the long division method or the synthetic division method. Suppose, we have a polynomial function f(x) with a linear divisor (x -a), the remainder theorem posits that the remainder is equal to the value of the polynomial function at the root of the linear factor.
Here, the divisor is (x - 6). Setting it to zero, we have:
x - 6 = 0
x = 6
Now, this can be used to determine the value of k in the given function;
f(x) = 3x² - 25x + k
- when x = 6, the remainder is zero;
So,
f(6) = 3(6)² - 25(6) + k
0 =108 - 150 + k
k = 42
Now, that the value of the constant is determined, then f(-3) can be computed as:
f(x) = 3x² - 25x + k
f(-3) = 3(-3)² - 25(-3) + 42
f(-3) = 27 + 75 + 42
f(-3) = 144
Therefore, we can conclude that the value of f(-3) in the given function is 144.