B. -3
The value of a for given polynomial is -3
<h3>
Explanation:</h3>
<em>Factor theorem for polynomials,</em>
<u><em>If (x-c) is a factor of polynomial f(x), then f(c)=0</em></u>
Given: x+a is a factor of polynomial 
Let 
By Factor theorem, since x+a is a factor of f(x),
![(x+a)=[x-(-a)]\\So,\ f(-a)=0](https://tex.z-dn.net/?f=%28x%2Ba%29%3D%5Bx-%28-a%29%5D%5C%5CSo%2C%5C%20f%28-a%29%3D0)
Substituting 
in f(x)=0, we get
![f(x) = 4x^3-13x^2-ax = 0\\f(-a)= [4(-a)^3]-[13(-a)^2]-[a(-a)] = 0\\(-4a^3-13a^2+a^2)=0\\(-4a^3-12a^2)=0\\-4a^3=12a^2\\\frac{a^3}{a^2} =\frac{12}{-4} \\\\a=(-3)](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%5E3-13x%5E2-ax%20%3D%200%5C%5Cf%28-a%29%3D%20%5B4%28-a%29%5E3%5D-%5B13%28-a%29%5E2%5D-%5Ba%28-a%29%5D%20%3D%200%5C%5C%28-4a%5E3-13a%5E2%2Ba%5E2%29%3D0%5C%5C%28-4a%5E3-12a%5E2%29%3D0%5C%5C-4a%5E3%3D12a%5E2%5C%5C%5Cfrac%7Ba%5E3%7D%7Ba%5E2%7D%20%3D%5Cfrac%7B12%7D%7B-4%7D%20%5C%5C%5C%5Ca%3D%28-3%29)
Therefore, value of a is (-3)
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