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 determine possible rational roots using the Rational Root Theorem?

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To find 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 4x^3 - 9x^2 + 2x + 1?

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±1, ±1/2, ±1/4.

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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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±1, ±7, ±1/3, ±7/3.

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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 of the form (x - c).

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How many zeros are needed in synthetic division for the polynomial x^6 + 4x^3 + 2?

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4 zeros are needed.

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What is the complete list of possible rational zeros for f(x) = 3x^3 + 2x^2 - 6x + 7?

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±1, ±7, ±1/3, ±7/3.

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

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±1, ±2, ±4, ±8.

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What is the order of polynomial coefficients when dividing (3x - 4x^3 + 6x^4 + 1) by (x + 3)?

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6, -4, 0, 3, 1.

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (indeterminates) raised to non-negative integer powers and coefficients.