Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x5−x
Evaluate
x5−x×1
Solution
x5−x
Show Solution
Factor the expression
x(x−1)(x+1)(x2+1)
Evaluate
x5−x×1
Any expression multiplied by 1 remains the same
x5−x
Factor out x from the expression
x(x4−1)
Factor the expression
More Steps
Evaluate
x4−1
Rewrite the expression in exponential form
(x2)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(x2−1)(x2+1)
x(x2−1)(x2+1)
Solution
More Steps
Evaluate
x2−1
Rewrite the expression in exponential form
x2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(x−1)(x+1)
x(x−1)(x+1)(x2+1)
Show Solution
Find the roots
x1=−1,x2=0,x3=1
Evaluate
x5−x×1
To find the roots of the expression,set the expression equal to 0
x5−x×1=0
Any expression multiplied by 1 remains the same
x5−x=0
Factor the expression
x(x4−1)=0
Separate the equation into 2 possible cases
x=0x4−1=0
Solve the equation
More Steps
Evaluate
x4−1=0
Move the constant to the right-hand side and change its sign
x4=0+1
Removing 0 doesn't change the value,so remove it from the expression
x4=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±41
Simplify the expression
x=±1
Separate the equation into 2 possible cases
x=1x=−1
x=0x=1x=−1
Solution
x1=−1,x2=0,x3=1
Show Solution