Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
3x2(1−x)(1+x+x2)(1+x)(1−x+x2)
Evaluate
3x2−3x8
Factor out 3x2 from the expression
3x2(1−x6)
Factor the expression
More Steps
Evaluate
1−x6
Rewrite the expression in exponential form
12−(x3)2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−x3)(1+x3)
3x2(1−x3)(1+x3)
Evaluate
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)
3x2(1−x)(1+x+x2)(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)
3x2(1−x)(1+x+x2)(1+x)(1−x+x2)
Show Solution
Find the roots
x1=−1,x2=0,x3=1
Evaluate
3x2−3x8
To find the roots of the expression,set the expression equal to 0
3x2−3x8=0
Factor the expression
3x2(1−x6)=0
Divide both sides
x2(1−x6)=0
Separate the equation into 2 possible cases
x2=01−x6=0
The only way a power can be 0 is when the base equals 0
x=01−x6=0
Solve the equation
More Steps
Evaluate
1−x6=0
Move the constant to the right-hand side and change its sign
−x6=0−1
Removing 0 doesn't change the value,so remove it from the expression
−x6=−1
Change the signs on both sides of the equation
x6=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±61
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