Question
Factor the expression
(x2−x+1)(x2+x+1)
Evaluate
x4+x2+1
Calculate
x4+x3+x2−x3−x2−x+x2+x+1
Rewrite the expression
x2×x2+x2×x+x2−x×x2−x×x−x+x2+x+1
Factor out x2 from the expression
x2(x2+x+1)−x×x2−x×x−x+x2+x+1
Factor out −x from the expression
x2(x2+x+1)−x(x2+x+1)+x2+x+1
Solution
(x2−x+1)(x2+x+1)
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Find the roots
x1=−21−23i,x2=−21+23i,x3=21−23i,x4=21+23i
Alternative Form
x1≈−0.5−0.866025i,x2≈−0.5+0.866025i,x3≈0.5−0.866025i,x4≈0.5+0.866025i
Evaluate
x4+x2+1
To find the roots of the expression,set the expression equal to 0
x4+x2+1=0
Factor the expression
(x2−x+1)(x2+x+1)=0
Separate the equation into 2 possible cases
x2−x+1=0x2+x+1=0
Solve the equation
More Steps

Evaluate
x2−x+1=0
Substitute a=1,b=−1 and c=1 into the quadratic formula x=2a−b±b2−4ac
x=21±(−1)2−4
Simplify the expression
More Steps

Evaluate
(−1)2−4
Evaluate the power
1−4
Subtract the numbers
−3
x=21±−3
Simplify the radical expression
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Evaluate
−3
Evaluate the power
3×−1
Evaluate the power
3×i
x=21±3×i
Separate the equation into 2 possible cases
x=21+3×ix=21−3×i
Simplify the expression
x=21+23ix=21−3×i
Simplify the expression
x=21+23ix=21−23i
x=21+23ix=21−23ix2+x+1=0
Solve the equation
More Steps

Evaluate
x2+x+1=0
Substitute a=1,b=1 and c=1 into the quadratic formula x=2a−b±b2−4ac
x=2−1±12−4
Simplify the expression
More Steps

Evaluate
12−4
1 raised to any power equals to 1
1−4
Subtract the numbers
−3
x=2−1±−3
Simplify the radical expression
More Steps

Evaluate
−3
Evaluate the power
3×−1
Evaluate the power
3×i
x=2−1±3×i
Separate the equation into 2 possible cases
x=2−1+3×ix=2−1−3×i
Simplify the expression
x=−21+23ix=2−1−3×i
Simplify the expression
x=−21+23ix=−21−23i
x=21+23ix=21−23ix=−21+23ix=−21−23i
Solution
x1=−21−23i,x2=−21+23i,x3=21−23i,x4=21+23i
Alternative Form
x1≈−0.5−0.866025i,x2≈−0.5+0.866025i,x3≈0.5−0.866025i,x4≈0.5+0.866025i
Show Solution
