Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−x+4x3
Evaluate
x2−164x3−x4
Factor the expression
x2−16−x3(x−4)
Factor the expression
(x−4)(x+4)−x3(x−4)
Reduce the fraction
x+4−x3
Solution
−x+4x3
Show Solution
Find the excluded values
x=4,x=−4
Evaluate
x2−164x3−x4
To find the excluded values,set the denominators equal to 0
x2−16=0
Move the constant to the right-hand side and change its sign
x2=0+16
Removing 0 doesn't change the value,so remove it from the expression
x2=16
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±16
Simplify the expression
More Steps
Evaluate
16
Write the number in exponential form with the base of 4
42
Reduce the index of the radical and exponent with 2
4
x=±4
Separate the equation into 2 possible cases
x=4x=−4
Solution
x=4,x=−4
Show Solution
Find the roots
x=0
Evaluate
x2−164x3−x4
To find the roots of the expression,set the expression equal to 0
x2−164x3−x4=0
Find the domain
More Steps
Evaluate
x2−16=0
Move the constant to the right side
x2=16
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±16
Simplify the expression
More Steps
Evaluate
16
Write the number in exponential form with the base of 4
42
Reduce the index of the radical and exponent with 2
4
x=±4
Separate the inequality into 2 possible cases
{x=4x=−4
Find the intersection
x∈(−∞,−4)∪(−4,4)∪(4,+∞)
x2−164x3−x4=0,x∈(−∞,−4)∪(−4,4)∪(4,+∞)
Calculate
x2−164x3−x4=0
Divide the terms
More Steps
Evaluate
x2−164x3−x4
Factor the expression
x2−16−x3(x−4)
Factor the expression
(x−4)(x+4)−x3(x−4)
Reduce the fraction
x+4−x3
Calculate
−x+4x3
−x+4x3=0
Rewrite the expression
x+4−x3=0
Cross multiply
−x3=(x+4)×0
Simplify the equation
−x3=0
Change the signs on both sides of the equation
x3=0
The only way a power can be 0 is when the base equals 0
x=0
Check if the solution is in the defined range
x=0,x∈(−∞,−4)∪(−4,4)∪(4,+∞)
Solution
x=0
Show Solution