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 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 for the polynomial f(x) = 2x^3 + 5x^2 - 9x + 5?

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The possible rational roots are ±1, 5, 1/2, and 5/2.

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What is a zero of a polynomial?

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A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Tags

CCSS.HSF-IF.C.7C

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

Tags

CCSS.HSF-IF.C.7C

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - c). It is used to find polynomial roots more efficiently.

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CCSS.HSA.APR.D.6

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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 other roots.

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What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

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What is the constant term in a polynomial?

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The constant term is the term in a polynomial that does not contain any variables, representing the value of the polynomial when all variable terms are zero.

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How do you factor a polynomial once a root is found?

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Once a root is found, you can use synthetic division to divide the polynomial by (x - root), resulting in a lower-degree polynomial that can be factored further.

Tags

CCSS.HSA.APR.B.2