Question

Answer q 13 and also explain.

Answer 1

(13).

Given f(x) = k^2x^3 - kx^2 + 3kx - k

Factor theorem states that if (x - a) is a factor of polynomial f(x), then f(a) = 0.

= > f(3) = k^2(3)^3 - k(3)^2 + 3k(3) - k

= > 0 = 27k^2  - 9k  + 9k - k

= > 0 = 27k^2 - k

= > 0 = k(27k - 1)

= > 27k - 1 = 0

= > k = 1/27.

Hope this helps!