Explanation: Since the solutions for \(f(x)=0\) are \(-2, 0\), and 3 , this means that \((x+2), x\), and \((x-3)\) are the only factors of the equation. So, the equation is \(x\times(x+2)\times(x-3)\). To find out the three solutions for \(f(x-2)=0\), we replace x with \((x-2)\) in the original equation. So, the equation becomes \((x-2)\times(x-2+2)\times(x-2-3)=(x-2)\times x\times(x-5)=x\times(x-2)\times(x-5)\). Thus, the three solutions for \(f(x-2)=0\) are 0,2 , and 5 .
