Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
−x(x−1)(x+1)(x2−6)
Evaluate
7x3−x5−6x
Evaluate
−x5+7x3−6x
Rewrite the expression
−x×x4+x×7x2−x×6
Factor out −x from the expression
−x(x4−7x2+6)
Factor the expression
More Steps
Evaluate
x4−7x2+6
Rewrite the expression
x4+(−6−1)x2+6
Calculate
x4−6x2−x2+6
Rewrite the expression
x2×x2−x2×6−x2+6
Factor out x2 from the expression
x2(x2−6)−x2+6
Factor out −1 from the expression
x2(x2−6)−(x2−6)
Factor out x2−6 from the expression
(x2−1)(x2−6)
−x(x2−1)(x2−6)
Solution
−x(x−1)(x+1)(x2−6)
Show Solution
Find the roots
x1=−6,x2=−1,x3=0,x4=1,x5=6
Alternative Form
x1≈−2.44949,x2=−1,x3=0,x4=1,x5≈2.44949
Evaluate
7x3−x5−6x
To find the roots of the expression,set the expression equal to 0
7x3−x5−6x=0
Factor the expression
−x(x−1)(x+1)(x2−6)=0
Separate the equation into 4 possible cases
−x=0x−1=0x+1=0x2−6=0
Change the signs on both sides of the equation
x=0x−1=0x+1=0x2−6=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=0x=1x+1=0x2−6=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=0x=1x=−1x2−6=0
Solve the equation
More Steps
Evaluate
x2−6=0
Move the constant to the right-hand side and change its sign
x2=0+6
Removing 0 doesn't change the value,so remove it from the expression
x2=6
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±6
Separate the equation into 2 possible cases
x=6x=−6
x=0x=1x=−1x=6x=−6
Solution
x1=−6,x2=−1,x3=0,x4=1,x5=6
Alternative Form
x1≈−2.44949,x2=−1,x3=0,x4=1,x5≈2.44949
Show Solution