Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(n−2)(n+2)(n2+2)
Evaluate
n4−2n2−8
Rewrite the expression
n4+(2−4)n2−8
Calculate
n4+2n2−4n2−8
Rewrite the expression
n2×n2+n2×2−4n2−4×2
Factor out n2 from the expression
n2(n2+2)−4n2−4×2
Factor out −4 from the expression
n2(n2+2)−4(n2+2)
Factor out n2+2 from the expression
(n2−4)(n2+2)
Solution
(n−2)(n+2)(n2+2)
Show Solution
Find the roots
n1=−2×i,n2=2×i,n3=−2,n4=2
Alternative Form
n1≈−1.414214i,n2≈1.414214i,n3=−2,n4=2
Evaluate
n4−2n2−8
To find the roots of the expression,set the expression equal to 0
n4−2n2−8=0
Factor the expression
(n−2)(n+2)(n2+2)=0
Separate the equation into 3 possible cases
n−2=0n+2=0n2+2=0
Solve the equation
More Steps
Evaluate
n−2=0
Move the constant to the right-hand side and change its sign
n=0+2
Removing 0 doesn't change the value,so remove it from the expression
n=2
n=2n+2=0n2+2=0
Solve the equation
More Steps
Evaluate
n+2=0
Move the constant to the right-hand side and change its sign
n=0−2
Removing 0 doesn't change the value,so remove it from the expression
n=−2
n=2n=−2n2+2=0
Solve the equation
More Steps
Evaluate
n2+2=0
Move the constant to the right-hand side and change its sign
n2=0−2
Removing 0 doesn't change the value,so remove it from the expression
n2=−2
Take the root of both sides of the equation and remember to use both positive and negative roots
n=±−2
Simplify the expression
More Steps
Evaluate
−2
Evaluate the power
2×−1
Evaluate the power
2×i
n=±(2×i)
Separate the equation into 2 possible cases
n=2×in=−2×i
n=2n=−2n=2×in=−2×i
Solution
n1=−2×i,n2=2×i,n3=−2,n4=2
Alternative Form
n1≈−1.414214i,n2≈1.414214i,n3=−2,n4=2
Show Solution