# Find the Roots/Zeros Using the Rational Roots Test x^4-2x^3+14x^2-8x+40

Factor the left side of the equation.
Regroup terms.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
Factor out of .
Factor out of .
Factor out of .
Reorder terms.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Subtract from both sides of the equation.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Move to the left of .
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set the next factor equal to and solve.
Set the next factor equal to .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Move to the left of .
Multiply by .
Simplify .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Move to the left of .
Multiply by .
Simplify .
Change the to .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Move to the left of .
Multiply by .
Simplify .
Change the to .
The final answer is the combination of both solutions.
The final solution is all the values that make true.
Find the Roots/Zeros Using the Rational Roots Test x^4-2x^3+14x^2-8x+40