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, is such that p is a factor of the constant term and q is a factor of the leading coefficient.

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How do you apply the Rational Root Theorem?

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1. Identify the constant term and leading coefficient of the polynomial. 2. List all factors of the constant term (p) and the leading coefficient (q). 3. Form all possible rational roots as p/q.

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What are the possible rational roots for the polynomial 2x^3 - 11x^2 + 12x + 9?

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±1, ±3, ±9, ±1/2, ±3/2, ±9/2.

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Solve using the Rational Root Theorem: x^3 - 7x - 6 = 0.

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The rational roots are -1, -2, and 3.

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What is the remainder when f(x) = 2x^4 - 3x^3 + x - 5 is divided by (x - 1)?

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The remainder is 3.

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If (x + 2) is a factor of f(x) = x^3 + 4x^2 + bx + 8, what is the value of b?

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The value of b is -4.

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What is a factor of a polynomial?

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A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor.

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How do you find the roots of a polynomial?

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To find the roots of a polynomial, you can use methods such as factoring, synthetic division, or applying the Rational Root Theorem.

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

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The constant term helps identify the possible rational roots since its factors are potential values for p in p/q.