Question
Factor the expression
x2(x−1−4x2)
Evaluate
x3−x2−4x4
Rewrite the expression
x2×x−x2−x2×4x2
Solution
x2(x−1−4x2)
Show Solution

Find the roots
x1=81−815i,x2=81+815i,x3=0
Alternative Form
x1≈0.125−0.484123i,x2≈0.125+0.484123i,x3=0
Evaluate
x3−x2−4x4
To find the roots of the expression,set the expression equal to 0
x3−x2−4x4=0
Factor the expression
x2(x−1−4x2)=0
Separate the equation into 2 possible cases
x2=0x−1−4x2=0
The only way a power can be 0 is when the base equals 0
x=0x−1−4x2=0
Solve the equation
More Steps

Evaluate
x−1−4x2=0
Rewrite in standard form
−4x2+x−1=0
Multiply both sides
4x2−x+1=0
Substitute a=4,b=−1 and c=1 into the quadratic formula x=2a−b±b2−4ac
x=2×41±(−1)2−4×4
Simplify the expression
x=81±(−1)2−4×4
Simplify the expression
More Steps

Evaluate
(−1)2−4×4
Evaluate the power
1−4×4
Multiply the numbers
1−16
Subtract the numbers
−15
x=81±−15
Simplify the radical expression
More Steps

Evaluate
−15
Evaluate the power
15×−1
Evaluate the power
15×i
x=81±15×i
Separate the equation into 2 possible cases
x=81+15×ix=81−15×i
Simplify the expression
x=81+815ix=81−15×i
Simplify the expression
x=81+815ix=81−815i
x=0x=81+815ix=81−815i
Solution
x1=81−815i,x2=81+815i,x3=0
Alternative Form
x1≈0.125−0.484123i,x2≈0.125+0.484123i,x3=0
Show Solution
