Fundamental Theorem of Algebra

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What does the degree of a polynomial indicate about its roots?

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The degree of a polynomial indicates the maximum number of roots (or zeros) it can have.

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How many zeros does a polynomial of degree n have?

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A polynomial of degree n has exactly n roots, counting multiplicities.

Tags

CCSS.HSN.CN.C.9

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What is the standard form of a polynomial?

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The standard form of a polynomial is when it is expressed as a sum of terms in descending order of their degrees.

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What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.

Tags

CCSS.HSN.CN.C.9

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How can you determine the degree of a polynomial?

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

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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.

Tags

CCSS.HSA.APR.B.2

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What does it mean if a polynomial has a root at x = r?

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If a polynomial has a root at x = r, it means that when x is substituted with r, the polynomial evaluates to zero.

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.

Tags

CCSS.HSA.APR.D.6

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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

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

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To verify if (x - c) is a factor of a polynomial, evaluate the polynomial at c. If f(c) = 0, then (x - c) is a factor.

Tags

CCSS.HSA.APR.B.2