If f(x)=x^3-12x^2+41x-30 and x-5 is a factor of f( f(x) algebraically. Answer Attempt 2 out of 2

To verify that $x-5$ is a factor of $f(x)$, we can use the Factor Theorem. According to the Factor Theorem, if $x-5$ is a factor of $f(x)$, then $f(5)$ should be equal to 0.<br /><br />Let's substitute $x=5$ into the function $f(x)$ and check if $f(5)$ equals 0:<br /><br />$f(5) = 5^3 - 12(5)^2 + 41(5) - 30$<br /><br />$f(5) = 125 - 300 + 205 - 30$<br /><br />$f(5) = -125 + 205 - 30$<br /><br />$f(5) = 80 - 30$<br /><br />$f(5) = 50$<br /><br />Since $f(5)$ is not equal to 0, $x-5$ is not a factor of $f(x)$.