Consider the following function.

Function

$f(x)=6x^3+47x^2-10x-16,(2x+1),(3x-2)$

$($a$)$ Verify the given factors of $f(x).$

$($b$)$ Find the remaining factor$($s$)$ of $f(x).($Enter your answers as a comma$-$separated list.$)$

$($c$)$ Use your results to write the complete factorization of $f(x).$

$f(x)=$

$($d$)$ List all real zeros of $f.($Enter your answers as a comma$-$separated list.$)$

$x=$