Question

Need help with question 3 just want to ensure my answer is correct before continuing

Answer 1

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 $4x^3-13x^2-ax$

Let $f(x) = 4x^3-13x^2-ax$

By Factor theorem, since x+a is a factor of f(x),

$(x+a)=[x-(-a)]\\So,\ f(-a)=0$

Substituting $x=-a$ in f(x)=0, we get

$f(x) = 4x^3-13x^2-ax = 0\\f(-a)= [4(-a)^3]-[13(-a)^2]-[a(-a)] = 0\\(-4a^3-13a^2+a^2)=0\\(-4a^3-12a^2)=0\\-4a^3=12a^2\\\frac{a^3}{a^2} =\frac{12}{-4} \\\\a=(-3)$

Therefore, value of a is (-3)