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