Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x−2)(x+2)(x2+2)
Evaluate
x4−2x2−8
Rewrite the expression
x4+(2−4)x2−8
Calculate
x4+2x2−4x2−8
Rewrite the expression
x2×x2+x2×2−4x2−4×2
Factor out x2 from the expression
x2(x2+2)−4x2−4×2
Factor out −4 from the expression
x2(x2+2)−4(x2+2)
Factor out x2+2 from the expression
(x2−4)(x2+2)
Solution
(x−2)(x+2)(x2+2)
Show Solution
Find the roots
x1=−2×i,x2=2×i,x3=−2,x4=2
Alternative Form
x1≈−1.414214i,x2≈1.414214i,x3=−2,x4=2
Evaluate
x4−2x2−8
To find the roots of the expression,set the expression equal to 0
x4−2x2−8=0
Factor the expression
(x−2)(x+2)(x2+2)=0
Separate the equation into 3 possible cases
x−2=0x+2=0x2+2=0
Solve the equation
More Steps
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+2=0x2+2=0
Solve the equation
More Steps
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=−2x2+2=0
Solve the equation
More Steps
Evaluate
x2+2=0
Move the constant to the right-hand side and change its sign
x2=0−2
Removing 0 doesn't change the value,so remove it from the expression
x2=−2
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±−2
Simplify the expression
More Steps
Evaluate
−2
Evaluate the power
2×−1
Evaluate the power
2×i
x=±(2×i)
Separate the equation into 2 possible cases
x=2×ix=−2×i
x=2x=−2x=2×ix=−2×i
Solution
x1=−2×i,x2=2×i,x3=−2,x4=2
Alternative Form
x1≈−1.414214i,x2≈1.414214i,x3=−2,x4=2
Show Solution