Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
k(1−k)(k4+k3+k2+k+1)
Evaluate
k−k6
Rewrite the expression
k−k×k5
Factor out k from the expression
k(1−k5)
Solution
More Steps
Evaluate
1−k5
Calculate
k4+k3+k2+k+1−k5−k4−k3−k2−k
Rewrite the expression
k4+k3+k2+k+1−k×k4−k×k3−k×k2−k×k−k
Factor out −k from the expression
k4+k3+k2+k+1−k(k4+k3+k2+k+1)
Factor out k4+k3+k2+k+1 from the expression
(1−k)(k4+k3+k2+k+1)
k(1−k)(k4+k3+k2+k+1)
Show Solution
Find the roots
k1=0,k2=1
Evaluate
k−k6
To find the roots of the expression,set the expression equal to 0
k−k6=0
Factor the expression
k(1−k5)=0
Separate the equation into 2 possible cases
k=01−k5=0
Solve the equation
More Steps
Evaluate
1−k5=0
Move the constant to the right-hand side and change its sign
−k5=0−1
Removing 0 doesn't change the value,so remove it from the expression
−k5=−1
Change the signs on both sides of the equation
k5=1
Take the 5-th root on both sides of the equation
5k5=51
Calculate
k=51
Simplify the root
k=1
k=0k=1
Solution
k1=0,k2=1
Show Solution