B. -3
The value of a for given polynomial is -3
Explanation:
Factor theorem for polynomials,
If (x-c) is a factor of polynomial f(x), then f(c)=0
Given: x+a is a factor of polynomial [tex]4x^3-13x^2-ax[/tex]
Let [tex]f(x) = 4x^3-13x^2-ax[/tex]
By Factor theorem, since x+a is a factor of f(x),
[tex](x+a)=[x-(-a)]\\So,\ f(-a)=0[/tex]
Substituting [tex]x=-a[/tex] in f(x)=0, we get
[tex]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)[/tex]
Therefore, value of a is (-3)
