Algebra 2, Unit 2: Polynomial Functions. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is a polynomial function?
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A function made of terms with non-negative integer exponents- What is the degree of a polynomial function?
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The highest exponent among its terms- What is the leading coefficient of a polynomial?
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The coefficient of the highest-degree term- What does the leading coefficient and degree tell you about a polynomial's end behavior?
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Whether the graph rises or falls at both ends- What is a cubic function?
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A polynomial function of degree 3- What is a quartic function?
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A polynomial function of degree 4- What is a zero (root) of a polynomial function?
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A value of x where the function equals zero- What is the Fundamental Theorem of Algebra?
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A polynomial of degree n has exactly n complex roots, counted with multiplicity- What is multiplicity of a root?
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The number of times a given root appears as a factor- What does an even multiplicity root do to a graph at that point?
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The graph touches the x-axis and turns back (does not cross)- What does an odd multiplicity root do to a graph at that point?
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The graph crosses through the x-axis- What is synthetic division used for?
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A shortcut method for dividing a polynomial by a linear binomial- What is the Remainder Theorem?
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Dividing a polynomial by (x - a) gives a remainder equal to f(a)- What is the Factor Theorem?
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(x - a) is a factor of f(x) if and only if f(a) = 0- What is the Rational Root Theorem used to find?
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Possible rational roots of a polynomial equation
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