Find the Roots (Zeros) x^4+2x^3-23x^2-24x+144=0

Math
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.
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Substitute into the polynomial.
Raise to the power of .
Raise to the power of .
Multiply by .
Add and .
Raise to the power of .
Multiply by .
Subtract from .
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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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 .
Raise to the power of .
Multiply by .
Add and .
Multiply by .
Subtract from .
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 perfect square rule.
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Factor using the perfect square rule.
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Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
Remove unnecessary parentheses.
Combine like factors.
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
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 .
Set the 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 .
Set the equal to .
Subtract from both sides of the equation.
The final solution is all the values that make true.
Find the Roots (Zeros) x^4+2x^3-23x^2-24x+144=0

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