Question

Find the value of k if x - 3 is a factor of $k^2{x}^3-k{x}^2$ -3kx - k

Answer 1

Let f(x) = $k^2{x}^3-k{x}^2$ -3kx - k

and Let x - 3 = 0, then x = 3

Now, f(3) = $k^2(3{)}^3-k(3{)}^2+3k\left(3\right)-k$

= $27k^2$ - 9k + 9k - k

= $27k^2$ - k

$\therefore$ x - 3 is a factor of f(x)

$\therefore$ Remainder = 0

$\therefore 27k^2$ - k = 0

$\Rightarrow k(27k-1)=0$

Either k = 0

or 27k - 1 = 0 $\Rightarrow$ 27k = 1

$\therefore k=\frac{1}{27}$