Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
x3(1−x)(1+x+x2)
Evaluate
x3−x6
Factor out x3 from the expression
x3(1−x3)
Solution
More Steps
Evaluate
1−x3
Rewrite the expression in exponential form
13−x3
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(1−x)(12+1×x+x2)
1 raised to any power equals to 1
(1−x)(1+1×x+x2)
Any expression multiplied by 1 remains the same
(1−x)(1+x+x2)
x3(1−x)(1+x+x2)
Show Solution
Find the roots
x1=0,x2=1
Evaluate
x3−x6
To find the roots of the expression,set the expression equal to 0
x3−x6=0
Factor the expression
x3(1−x3)=0
Separate the equation into 2 possible cases
x3=01−x3=0
The only way a power can be 0 is when the base equals 0
x=01−x3=0
Solve the equation
More Steps
Evaluate
1−x3=0
Move the constant to the right-hand side and change its sign
−x3=0−1
Removing 0 doesn't change the value,so remove it from the expression
−x3=−1
Change the signs on both sides of the equation
x3=1
Take the 3-th root on both sides of the equation
3x3=31
Calculate
x=31
Simplify the root
x=1
x=0x=1
Solution
x1=0,x2=1
Show Solution