Rational Root Theorem

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What is the Rational Root Theorem?

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The Rational Root Theorem states that any rational solution (or root) of a polynomial equation, in the form of p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient.

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How do you find the possible rational roots of a polynomial?

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To find the possible rational roots, list all factors of the constant term (p) and all factors of the leading coefficient (q). The possible rational roots are then the combinations of these factors in the form ±p/q.

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What are the possible rational roots of the polynomial f(x) = 2x^3 - 11x^2 + 12x + 9?

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The possible rational roots are ±1, ±3, ±9, ±1/2, ±3/2, ±9/2.

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What is a complete list of possible rational zeros for f(x) = x^3 + 2x^2 - 6x + 8?

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The complete list of possible rational zeros is ±1, ±2, ±4, ±8.

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If a polynomial has a leading coefficient of 3 and a constant term of 7, what are the possible rational roots?

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The possible rational roots are ±1, ±7, ±1/3, ±7/3.

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What does it mean for a rational root to 'work' in a polynomial?

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A rational root 'works' if substituting it into the polynomial results in a value of zero.

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How can you verify if a number is a root of a polynomial?

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To verify if a number is a root, substitute it into the polynomial equation and check if the result equals zero.

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What is the significance of the constant term in the Rational Root Theorem?

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The constant term is significant because its factors provide the possible values for p in the rational root p/q.

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What is the significance of the leading coefficient in the Rational Root Theorem?

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The leading coefficient is significant because its factors provide the possible values for q in the rational root p/q.

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What is the Rational Root Theorem used for?

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The Rational Root Theorem is used to identify potential rational roots of polynomial equations, aiding in the process of finding actual roots.