Question

For what value of a (x-5) is a factor of $x^3-3x^2$ + ax - 10?

Answer 1

f(x) = $x^3-3x^2$ + ax - 10

Let x - 5 = 0, then x = 5

Now, f(5) $=(5{)}^3-3(5{)}^2+a\times$ 5 - 10

= 125 - 75 + 5a - 10

= 125 - 85 + 5a = 40 + 5a

$\therefore$ (x-5) is a factor of f(x)

$\therefore$ Remainder = 0

$\Rightarrow$ 40 + 5a = 0 $\Rightarrow$ 5a = - 40

$\Rightarrow a=\frac{-40}{5}$= - 8

Hence a = - 8