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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.

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