Use the remainder theorem to find the remainder when $f(x)$ is divided by $x-3$. Then use the factor theorem to determine whether $x-3$ is $a$ factor of $f(x)$. \[ f(x)=2 x^{3}-10 x^{2}+10 x+10 \] The remainder is $\square$. Is $x-3$ a tactor of $f(x)=2 x^{3}-10 x^{2}+10 x+10$ ? Yes No

Step 1 ：Given the polynomial function \(f(x)=2 x^{3}-10 x^{2}+10 x+10\), we are asked to find the remainder when \(f(x)\) is divided by \(x-3\) and determine whether \(x-3\) is a factor of \(f(x)\).

Step 2 ：We use the remainder theorem which states that the remainder of a polynomial \(f(x)\) divided by \((x-a)\) is \(f(a)\). So, to find the remainder of \(f(x)\) divided by \((x-3)\), we substitute \(x=3\) into the polynomial.

Step 3 ：The remainder when \(f(x)\) is divided by \((x-3)\) is 4.

Step 4 ：According to the factor theorem, if the remainder is zero, then \((x-3)\) is a factor of \(f(x)\). If the remainder is not zero, then \((x-3)\) is not a factor of \(f(x)\).

Step 5 ：Since the remainder is not zero, \((x-3)\) is not a factor of \(f(x)\).

Step 6 ：Final Answer: The remainder is \(\boxed{4}\). No, \(x-3\) is not a factor of \(f(x)=2 x^{3}-10 x^{2}+10 x+10\).