Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x+1)(x2−x+1)(x2+x+1)
Evaluate
x5+x4+x3+x2+x+1
Evaluate
x5+x3+x+x4+x2+1
Rewrite the expression
x×x4+x×x2+x+x4+x2+1
Factor out x from the expression
x(x4+x2+1)+x4+x2+1
Factor out x4+x2+1 from the expression
(x+1)(x4+x2+1)
Solution
More Steps
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
Factor out x2+x+1 from the expression
(x2−x+1)(x2+x+1)
(x+1)(x2−x+1)(x2+x+1)
Show Solution
Find the roots
x1=−21−23i,x2=−21+23i,x3=21−23i,x4=21+23i,x5=−1
Alternative Form
x1≈−0.5−0.866025i,x2≈−0.5+0.866025i,x3≈0.5−0.866025i,x4≈0.5+0.866025i,x5=−1
Evaluate
x5+x4+x3+x2+x+1
To find the roots of the expression,set the expression equal to 0
x5+x4+x3+x2+x+1=0
Factor the expression
(x+1)(x2−x+1)(x2+x+1)=0
Separate the equation into 3 possible cases
x+1=0x2−x+1=0x2+x+1=0
Solve the equation
More Steps
Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
x=−1x2−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
More Steps
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=−1x=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=−1x=21+23ix=21−23ix=−21+23ix=−21−23i
Solution
x1=−21−23i,x2=−21+23i,x3=21−23i,x4=21+23i,x5=−1
Alternative Form
x1≈−0.5−0.866025i,x2≈−0.5+0.866025i,x3≈0.5−0.866025i,x4≈0.5+0.866025i,x5=−1
Show Solution