Answer: -86
Given:
[tex]P(x)=2x^3-11x^2+ax-40[/tex]
If we consider x+4 as a factor of the given polynomial, this would mean that x=-4. For an x- value to be a factor of a polynomial, P(x) must be equal to 0. With that, we will have:
[tex]\begin{gathered} P(-4)=0 \\ P(-4)=2x^3-11x^2+ax-40 \\ 0=2(-4)^3-11(-4)^2+a(-4)-40 \\ 0=-128-176-4a-40 \\ 4a=-128-176-40 \\ 4a=-344 \\ a=-86 \end{gathered}[/tex]
Therefore, the answer is -86
