Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x−2)(x+1)(x2−x+1)(x2+2x+4)
Evaluate
x6−7x3−8
Calculate
x6+2x5+4x4+x3+2x2+4x−2x5−4x4−8x3−2x2−4x−8
Rewrite the expression
x×x5+x×2x4+x×4x3+x×x2+x×2x+x×4−2x5−2×2x4−2×4x3−2x2−2×2x−2×4
Factor out x from the expression
x(x5+2x4+4x3+x2+2x+4)−2x5−2×2x4−2×4x3−2x2−2×2x−2×4
Factor out −2 from the expression
x(x5+2x4+4x3+x2+2x+4)−2(x5+2x4+4x3+x2+2x+4)
Factor out x5+2x4+4x3+x2+2x+4 from the expression
(x−2)(x5+2x4+4x3+x2+2x+4)
Factor the expression
More Steps
Evaluate
x5+2x4+4x3+x2+2x+4
Calculate
x5+x4+3x3−2x2+4x+x4+x3+3x2−2x+4
Rewrite the expression
x×x4+x×x3+x×3x2−x×2x+x×4+x4+x3+3x2−2x+4
Factor out x from the expression
x(x4+x3+3x2−2x+4)+x4+x3+3x2−2x+4
Factor out x4+x3+3x2−2x+4 from the expression
(x+1)(x4+x3+3x2−2x+4)
(x−2)(x+1)(x4+x3+3x2−2x+4)
Solution
More Steps
Evaluate
x4+x3+3x2−2x+4
Calculate
x4+2x3+4x2−x3−2x2−4x+x2+2x+4
Rewrite the expression
x2×x2+x2×2x+x2×4−x×x2−x×2x−x×4+x2+2x+4
Factor out x2 from the expression
x2(x2+2x+4)−x×x2−x×2x−x×4+x2+2x+4
Factor out −x from the expression
x2(x2+2x+4)−x(x2+2x+4)+x2+2x+4
Factor out x2+2x+4 from the expression
(x2−x+1)(x2+2x+4)
(x−2)(x+1)(x2−x+1)(x2+2x+4)
Show Solution
Find the roots
x1=−1−3×i,x2=−1+3×i,x3=21−23i,x4=21+23i,x5=−1,x6=2
Alternative Form
x1≈−1−1.732051i,x2≈−1+1.732051i,x3≈0.5−0.866025i,x4≈0.5+0.866025i,x5=−1,x6=2
Evaluate
x6−7x3−8
To find the roots of the expression,set the expression equal to 0
x6−7x3−8=0
Factor the expression
(x−2)(x+1)(x2−x+1)(x2+2x+4)=0
Separate the equation into 4 possible cases
x−2=0x+1=0x2−x+1=0x2+2x+4=0
Solve the equation
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Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2x+1=0x2−x+1=0x2+2x+4=0
Solve the equation
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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=2x=−1x2−x+1=0x2+2x+4=0
Solve the equation
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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=2x=−1x=21+23ix=21−23ix2+2x+4=0
Solve the equation
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Evaluate
x2+2x+4=0
Substitute a=1,b=2 and c=4 into the quadratic formula x=2a−b±b2−4ac
x=2−2±22−4×4
Simplify the expression
More Steps
Evaluate
22−4×4
Multiply the numbers
22−16
Evaluate the power
4−16
Subtract the numbers
−12
x=2−2±−12
Simplify the radical expression
More Steps
Evaluate
−12
Evaluate the power
12×−1
Evaluate the power
12×i
Evaluate the power
23×i
x=2−2±23×i
Separate the equation into 2 possible cases
x=2−2+23×ix=2−2−23×i
Simplify the expression
x=−1+3×ix=2−2−23×i
Simplify the expression
x=−1+3×ix=−1−3×i
x=2x=−1x=21+23ix=21−23ix=−1+3×ix=−1−3×i
Solution
x1=−1−3×i,x2=−1+3×i,x3=21−23i,x4=21+23i,x5=−1,x6=2
Alternative Form
x1≈−1−1.732051i,x2≈−1+1.732051i,x3≈0.5−0.866025i,x4≈0.5+0.866025i,x5=−1,x6=2
Show Solution