Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
x3(x−1)(x+1)
Evaluate
x5−x3
Factor out x3 from the expression
x3(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)
x3(x−1)(x+1)
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Find the roots
x1=−1,x2=0,x3=1
Evaluate
x5−x3
To find the roots of the expression,set the expression equal to 0
x5−x3=0
Factor the expression
x3(x2−1)=0
Separate the equation into 2 possible cases
x3=0x2−1=0
The only way a power can be 0 is when the base equals 0
x=0x2−1=0
Solve the equation
More Steps
Evaluate
x2−1=0
Move the constant to the right-hand side and change its sign
x2=0+1
Removing 0 doesn't change the value,so remove it from the expression
x2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±1
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