Question
Factor the expression
Factor
(x−3)(x−2)(x+2)(x+3)
Evaluate
x4−13x2+36
Rewrite the expression
x4+(−4−9)x2+36
Calculate
x4−4x2−9x2+36
Rewrite the expression
x2×x2−x2×4−9x2+9×4
Factor out x2 from the expression
x2(x2−4)−9x2+9×4
Factor out −9 from the expression
x2(x2−4)−9(x2−4)
Factor out x2−4 from the expression
(x2−9)(x2−4)
Use a2−b2=(a−b)(a+b) to factor the expression
(x−3)(x+3)(x2−4)
Use a2−b2=(a−b)(a+b) to factor the expression
(x−3)(x+3)(x−2)(x+2)
Solution
(x−3)(x−2)(x+2)(x+3)
Show Solution
Find the roots
Find the roots of the algebra expression
x1=−3,x2=−2,x3=2,x4=3
Evaluate
x4−13x2+36
To find the roots of the expression,set the expression equal to 0
x4−13x2+36=0
Factor the expression
(x−3)(x−2)(x+2)(x+3)=0
Separate the equation into 4 possible cases
x−3=0x−2=0x+2=0x+3=0
Solve the equation
More Steps
Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=3x−2=0x+2=0x+3=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=3x=2x+2=0x+3=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=3x=2x=−2x+3=0
Solve the equation
More Steps
Evaluate
x+3=0
Move the constant to the right-hand side and change its sign
x=0−3
Removing 0 doesn't change the value,so remove it from the expression
x=−3
x=3x=2x=−2x=−3
Solution
x1=−3,x2=−2,x3=2,x4=3
Show Solution