1. f(3) = -69. 2. f(x) * g(x) = -60x^4 + 2070x^2 - 1380x + 1386. 3. f(x) / g(x) = (-30x^2 + 60x + 21) / (2x^2 - 69).
Substituting x = 3 into the function f(x) = -30x^2 + 60x + 21, we get f(3) = -30(3)^2 + 60(3) + 21 = -270 + 180 + 21 = -69.
To find f(x) * g(x), we multiply the two functions: (-30x^2 + 60x + 21) * (2x^2 - 69) = -60x^4 + 2070x^2 - 1380x + 1386.
To find f(x) / g(x), we divide f(x) by g(x): (-30x^2 + 60x + 21) / (2x^2 - 69). This expression cannot be further simplified, so the division is the final answer.
The probable question may be:
Consider the functions \(f(x) = -30x^2 + 60x + 21\) and \(g(x) = 2x^2 - 69\). Perform the following simplifications:
1. Evaluate \(f(3)\): Substitute \(x = 3\) into the function \(f(x)\) and compute the result.
2. Find \(f(x) \cdot g(x)\): Multiply the two given functions \(f(x)\) and \(g(x)\) to obtain the product function.
3. Determine \(\frac{f(x)}{g(x)}\): Divide \(f(x)\) by \(g(x)\) and simplify the resulting expression.