# Find the Roots (Zeros) x^4-2x^2-16x-15=0 Factor the left side of the equation.
Regroup terms.
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 .
Reorder and .
Factor out of .
Factor out of .
Factor out of .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by by adding the exponents.
Move .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Reorder terms.
Factor.
Rewrite in a factored form.
Factor using the rational roots test.
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Substitute into the polynomial.
Raise to the power of .
Multiply by .
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Divide by .
Write as a set of factors.
Factor using the rational roots test.
Factor using the rational roots test.
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Substitute into the polynomial.
Raise to the power of .
Multiply by .
Raise to the power of .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Divide by .
Write as a set of factors.
Remove unnecessary parentheses.
Remove unnecessary parentheses.
Multiply each term in by
Multiply each term in by .
Simplify .
Simplify by multiplying through.
Apply the distributive property.
Multiply by .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Rewrite as .
Multiply by .
Subtract from .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
Simplify each term.
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Simplify terms.
Combine the opposite terms in .
Subtract from .
Subtract from .
Subtract from .
Subtract from .
Apply the distributive property.
Simplify.
Move to the left of .
Multiply by .
Multiply by .
Multiply by .
Rewrite as .
Multiply by .
Factor the left side of the equation.
Factor using the rational roots test.
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Substitute into the polynomial.
Raise to the power of .
Multiply by .
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Divide by .
Write as a set of factors.
Factor using the rational roots test.
Factor using the rational roots test.
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Substitute into the polynomial.
Raise to the power of .
Multiply by .
Raise to the power of .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Divide by .
Write as a set of factors.
Remove unnecessary parentheses.
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.
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
Set the next factor equal to .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Multiply each term in by
Multiply each term in by .
Simplify .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Apply the distributive property.
Simplify.
Multiply .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
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) x^4-2x^2-16x-15=0

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