Algebra
Calculus
Trigonometry
Matrix
Question :
x^12-x^9
Factor the expression
x9(x−1)(x2+x+1)
Evaluate
x12−x9
Factor out x9 from the expression
x9(x3−1)
Solution
More Steps
Evaluate
x3−1
Rewrite the expression in exponential form
x3−13
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(x−1)(x2+x×1+12)
Any expression multiplied by 1 remains the same
(x−1)(x2+x+12)
1 raised to any power equals to 1
(x−1)(x2+x+1)
x9(x−1)(x2+x+1)
Show Solution
Find the roots
x1=0,x2=1
Evaluate
x12−x9
To find the roots of the expression,set the expression equal to 0
x12−x9=0
Factor the expression
x9(x3−1)=0
Separate the equation into 2 possible cases
x9=0x3−1=0
The only way a power can be 0 is when the base equals 0
x=0x3−1=0
Solve the equation
More Steps
Evaluate
x3−1=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
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
