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Use the Rational Roots Theorem to solve the equation for the rational roots

x3 - 3x2 + 4x - 12 = 0

Hi Ashley, I will be glad to help you.

The rational roots theorem says that if a polynomial with integer coefficients has rational roots they would be of the form + c/a where c is a factor of the constant term, here -12, and a is the factor of the leading coefficient, here 1.  Since the leading coefficient is 1, we do not need to worry about any fractional roots.  Any integer roots would be a plus or minus factor of 12.  Thus, all possible rational roots are -1, 1, -2, 2, -3, 3, -4, 4, -6, 6, -12, 12.  Using your calculator, you can find one root and then use synthetic division to factor out that root and get a quadratic equation, on which you could use the quadratic formula.

The polynomial x3 - 3x2 + 4x -12 nicely factors by grouping

x3 - 3x2 + 4x -12
x2(x - 3) + 4(x - 3)
(x2 + 4)(x - 3)

The integer root is 3

I hope this helps



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Anne Losch


Solving equations, graphing, evaluatin equations, factoring, functions, systems of equations, rational equations, exponent, complex numbers, word problems, logarithms, polynomials, and all topics in an Algebra 1, Algebra 2, or College Algebra class


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