Factor $f(x)=3 x^{3}+7 x^{2}-155 x+225$ into linear factors given that -9 is a zero of $f(x)$.

Step 1 ：Given the polynomial function \(f(x)=3 x^{3}+7 x^{2}-155 x+225\) and -9 is a zero of \(f(x)\), it means that \((x+9)\) is a factor of the polynomial.

Step 2 ：We can use polynomial division to divide the given polynomial by \((x+9)\) to find the other factors.

Step 3 ：The quotient from the polynomial division is another polynomial of degree 2, which is \(3x^2 - 20x + 25\). This is a quadratic polynomial and can be factored further into linear factors.

Step 4 ：The quadratic polynomial \(3x^2 - 20x + 25\) can be factored into \((x - 5)(3x - 5)\).

Step 5 ：Finally, the polynomial \(f(x)=3 x^{3}+7 x^{2}-155 x+225\) can be factored into linear factors as \(\boxed{(x+9)(x-5)(3x-5)}\).