Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x−3)(x+3)(x2+5)
Evaluate
x4−4x2−45
Rewrite the expression
x4+(5−9)x2−45
Calculate
x4+5x2−9x2−45
Rewrite the expression
x2×x2+x2×5−9x2−9×5
Factor out x2 from the expression
x2(x2+5)−9x2−9×5
Factor out −9 from the expression
x2(x2+5)−9(x2+5)
Factor out x2+5 from the expression
(x2−9)(x2+5)
Solution
(x−3)(x+3)(x2+5)
Show Solution
Find the roots
x1=−5×i,x2=5×i,x3=−3,x4=3
Alternative Form
x1≈−2.236068i,x2≈2.236068i,x3=−3,x4=3
Evaluate
x4−4x2−45
To find the roots of the expression,set the expression equal to 0
x4−4x2−45=0
Factor the expression
(x−3)(x+3)(x2+5)=0
Separate the equation into 3 possible cases
x−3=0x+3=0x2+5=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+3=0x2+5=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=−3x2+5=0
Solve the equation
More Steps
Evaluate
x2+5=0
Move the constant to the right-hand side and change its sign
x2=0−5
Removing 0 doesn't change the value,so remove it from the expression
x2=−5
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±−5
Simplify the expression
More Steps
Evaluate
−5
Evaluate the power
5×−1
Evaluate the power
5×i
x=±(5×i)
Separate the equation into 2 possible cases
x=5×ix=−5×i
x=3x=−3x=5×ix=−5×i
Solution
x1=−5×i,x2=5×i,x3=−3,x4=3
Alternative Form
x1≈−2.236068i,x2≈2.236068i,x3=−3,x4=3
Show Solution