Question

1. $k^3 - 11k^2 + 18k$

Explanation:

Step1: Factor out common term

$k^3 - 11k^2 + 18k = k(k^2 - 11k + 18)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $18$ and add to $-11$: $-2$ and $-9$.
$k^2 - 11k + 18 = (k - 2)(k - 9)$

Step3: Combine factors

Substitute the factored quadratic back.
$k(k^2 - 11k + 18) = k(k - 2)(k - 9)$

Answer:

$k(k - 2)(k - 9)$