Find the Roots (Zeros) x^4-2x^2-16x-15=0

Math
Factor the left side of the equation.
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Regroup terms.
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
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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 .
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Reorder and .
Factor out of .
Factor out of .
Factor out of .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by by adding the exponents.
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Move .
Use the power rule to combine exponents.
Add and .
Multiply by .
Multiply by .
Add and .
Reorder terms.
Factor.
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Rewrite in a factored form.
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Factor using the rational roots test.
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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.
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Substitute into the polynomial.
Raise to the power of .
Multiply by .
Raise to the power of .
Multiply by .
Add and .
Multiply by .
Subtract from .
Add and .
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.
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Factor using the rational roots test.
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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.
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Substitute into the polynomial.
Raise to the power of .
Multiply by .
Raise to the power of .
Add and .
Add and .
Add and .
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
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Multiply each term in by .
Simplify .
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Simplify by multiplying through.
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Apply the distributive property.
Multiply by .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by by adding the exponents.
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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.
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Simplify each term.
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Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Add and .
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
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Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
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Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Simplify terms.
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Combine the opposite terms in .
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Subtract from .
Add and .
Subtract from .
Subtract from .
Subtract from .
Apply the distributive property.
Simplify.
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Move to the left of .
Multiply by .
Multiply by .
Multiply by .
Rewrite as .
Multiply by .
Factor the left side of the equation.
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Factor using the rational roots test.
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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.
Tap for more steps…
Substitute into the polynomial.
Raise to the power of .
Multiply by .
Raise to the power of .
Multiply by .
Add and .
Multiply by .
Subtract from .
Add and .
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.
Tap for more steps…
Factor using the rational roots test.
Tap for more steps…
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.
Tap for more steps…
Substitute into the polynomial.
Raise to the power of .
Multiply by .
Raise to the power of .
Add and .
Add and .
Add and .
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.
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Set the first factor equal to .
Subtract from both sides of the equation.
Set the next factor equal to and solve.
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Set the next factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
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Set the next factor equal to .
Factor out of .
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Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Multiply each term in by
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Multiply each term in by .
Simplify .
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Apply the distributive property.
Simplify.
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Multiply by .
Multiply by .
Apply the distributive property.
Simplify.
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Multiply .
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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.
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Simplify the numerator.
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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 .
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Simplify the numerator.
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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 .
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Simplify the numerator.
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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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