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

Tags

CCSS.HSA.APR.B.2

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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 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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±1, ±3, ±9, ±1/2, ±3/2, ±9/2.

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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).

Tags

CCSS.HSA.APR.D.6

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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.

Tags

CCSS.HSA.APR.D.6

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What does it mean if (x - 2) is a factor of a polynomial?

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If (x - 2) is a factor of a polynomial, it means that when the polynomial is divided by (x - 2), the remainder is zero.

Tags

CCSS.HSA.APR.B.2

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What is the significance of finding rational roots in polynomial equations?

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Finding rational roots helps in factoring the polynomial, which can simplify solving the equation and finding all roots.

Tags

CCSS.HSA.APR.B.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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±1, ±2, ±4, ±8.

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How do 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. If the result is zero, then it is a root.

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What is the remainder theorem?

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The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Tags

CCSS.HSA.APR.B.2