Fundamental Theorem of Algebra

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What does the Fundamental Theorem of Algebra state?

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Every non-constant polynomial equation of degree n has exactly n complex roots, counting multiplicities.

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CCSS.HSN.CN.C.9

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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.

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CCSS.HSF-IF.C.7C

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If a polynomial has a complex zero, what can be said about its conjugate?

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The conjugate of a complex zero is also a zero of the polynomial.

Tags

CCSS.HSN.CN.C.9

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What is synthetic division?

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

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CCSS.HSA.APR.D.6

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How do you determine the degree of a polynomial?

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The degree of a polynomial is determined by the largest exponent of its variable.

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What is the relationship between the degree of a polynomial and the number of zeros?

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The degree of a polynomial indicates the maximum number of zeros it can have.

Tags

CCSS.HSN.CN.C.9

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient affects the end behavior of the polynomial graph.

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What does it mean for a polynomial to be factored completely?

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A polynomial is factored completely when it is expressed as a product of irreducible polynomials.

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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 f(c).

Tags

CCSS.HSA.APR.B.2

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How can you verify if (x - c) is a factor of a polynomial?

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If f(c) = 0, then (x - c) is a factor of the polynomial f(x).

Tags

CCSS.HSA.APR.B.2