Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
x4(1−x)(1+x)
Evaluate
x4−x6
Factor out x4 from the expression
x4(1−x2)
Solution
More Steps
Evaluate
1−x2
Rewrite the expression in exponential form
12−x2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−x)(1+x)
x4(1−x)(1+x)
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Find the roots
x1=−1,x2=0,x3=1
Evaluate
x4−x6
To find the roots of the expression,set the expression equal to 0
x4−x6=0
Factor the expression
x4(1−x2)=0
Separate the equation into 2 possible cases
x4=01−x2=0
The only way a power can be 0 is when the base equals 0
x=01−x2=0
Solve the equation
More Steps
Evaluate
1−x2=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
Change the signs on both sides of the equation
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
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