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find all holes of the following function. if a hole exists, write your answer as a coordinate point in simplest form.
\\( f(x) = \frac{5x^2 + 33x - 56}{3x^2 + 3x} \\)

Explanation:

Step1: Factor numerator and denominator

First, factor the numerator \(5x^{2}+33x - 56\). We need two numbers that multiply to \(5\times(-56)=-280\) and add to \(33\). The numbers are \(40\) and \(-7\). So,

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Next, factor the denominator \(3x^{2}+3x = 3x(x + 1)\).

Step2: Identify common factors

For a rational function, a hole occurs when there is a common factor in the numerator and the denominator. Here, the numerator is \((5x - 7)(x + 8)\) and the denominator is \(3x(x + 1)\). There are no common factors between the numerator and the denominator.

Answer:

There are no holes in the function \(f(x)=\frac{5x^{2}+33x - 56}{3x^{2}+3x}\)