Answer:
11k^2(k−7)(k−1)
Explanation:
11k^4 − 88k^3 + 77k^2
Factor out 11.
11(k^4-8k^3+7k^2)
Consider k^4-8k^3+7k^2. Factor out k^2.
k^2(k^2−8k+7)
Consider k^2 −8k+7. Factor the expression by grouping. First, the expression needs to be rewritten as k^2+ak+bk+7. To find a and b, set up a system to be solved.
a+b=−8
ab=1×7=7
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.
a=−7
b=−1
Rewrite k^2−8k+7 as (k^2−7k)+(−k+7).
(k^2−7k)+(−k+7)
Factor out k in the first and −1 in the second group.
k(k−7)−(k−7)
Factor out common term k−7 by using distributive property.
(k−7)(k−1)
Rewrite the complete factored expression.
11k^2(k−7)(k−1)