Problem
Use synthetic division to find the function values. Then check your work using a graphing calculator. $f(x)=x^{3}-13 x^{2}+52 x-60$; find $f(2), f(-5)$, and $f(6)$. \[ \begin{array}{l} f(2)=\square \\ f(-5)=\square \\ \text { (Simplify your answer.) } \\ f(6)=\square \\ \text { (Simplify your answer.) } \\ \end{array} \] (Simplify your answer.)
Solution
Step 1 ：Substitute the values into the function $f(x)=x^{3}-13 x^{2}+52 x-60$ and simplify the result.
Step 2 ：For $f(2)$, we get $2^{3}-13(2)^{2}+52(2)-60 = 0$
Step 3 ：For $f(-5)$, we get $(-5)^{3}-13(-5)^{2}+52(-5)-60 = -770$
Step 4 ：For $f(6)$, we get $6^{3}-13(6)^{2}+52(6)-60 = 0$
Step 5 ：So, the final answers are: $f(2)=\boxed{0}$, $f(-5)=\boxed{-770}$, and $f(6)=\boxed{0}$
