Answer
$A=-\frac{7}{2}$
Work Step by Step
We plug in $x=2$ to $f(x)$ to get
$f(2)=2\cdot2^3+A\cdot2^2+4\cdot2-5
\\5=2(8)+A(4)+8-5
\\5=16+4A+3
\\5=4A+19
\\5-19=4A
\\-14=4A
\\-\frac{14}{4}=\frac{4A}{4}
\\-\frac{7}{2}=A$
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