Understanding the degree of a polynomial is crucial in algebra, indicating the highest variable power in a term. Polynomials are classified by degree into constants, linear, quadratic, cubic, quartic, and quintic. The text also explores the zero polynomial, homogeneous polynomials, and the organization of polynomial terms. Additionally, it discusses the types of polynomials based on the number of terms and the coefficients, as well as the distinction between univariate and multivariate polynomials.
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1
Degree of a term with multiple variables
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2
Degree of a polynomial
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3
Identifying polynomial's leading term
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4
A polynomial with a degree of ______ is known as a constant polynomial.
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5
The term for a polynomial of degree ______ is a linear polynomial.
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6
A polynomial of degree two is referred to as a ______ polynomial.
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7
A ______ polynomial is the name given to a polynomial with a degree of three.
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8
Polynomials with degrees four and five are called ______ and ______ polynomials, respectively.
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9
Polynomials of degrees higher than five do not possess ______ names.
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10
A parabola is the graphical representation of a ______ polynomial, which can have at most two real roots.
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11
Degree of zero polynomial
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Undefined or assigned negative values like -1 or -∞
12
Reason for zero polynomial's infinite roots
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Equal to zero for all variable values
13
Homogeneity criteria for polynomials
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All terms have the same degree
14
The ______ property of addition allows polynomials to be written with terms in any sequence.
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commutative
15
Univariate polynomials are typically arranged in ______ order of their degrees.
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descending
16
Terms in a polynomial that have the same variables and exponents are known as ______ terms.
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17
Combining like terms by adding their coefficients may result in terms with a ______ coefficient.
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18
When terms have a zero coefficient, they are usually ______ from the polynomial.
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19
Definition: Monomial
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20
Polynomial term structure: Binomial vs. Trinomial
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21
A polynomial with ______ coefficients will only produce outputs that are also ______ when given real inputs.
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22
Definition of a bivariate polynomial
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23
Subtraction of polynomials effect on variables
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24
Importance of classifying polynomials by variables
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Legendre Polynomials
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