Classifying Polynomials Flashcards

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Questions and Answers

What is a monomial?

an expression with three terms

a polynomial with degree of zero

an expression with one term (correct)

an expression with two terms

What is a binomial?

an expression with two terms (correct)

an expression with three terms

a polynomial with degree of 1

an expression with one term

What is a trinomial?

an expression with three terms (correct)

an expression with two terms

an expression with one term

a polynomial with degree of 4

What defines a polynomial?

both A and B Signup and view all the answers

What is a constant?

a polynomial with a degree of zero Signup and view all the answers

What degree does a linear polynomial have?

degree of 1 Signup and view all the answers

What degree does a quadratic polynomial have?

degree of 2 Signup and view all the answers

What degree does a cubic polynomial have?

degree of 3 Signup and view all the answers

What degree does a quartic polynomial have?

degree of 4 Signup and view all the answers

What degree does a quintic polynomial have?

degree of 5 Signup and view all the answers

What does nth degree refer to?

any polynomial with a degree higher than 5 Signup and view all the answers

What is the degree of the monomial 5a³b²c?

6 Signup and view all the answers

What is the classification of the polynomial 4x - 2x²?

quadratic binomial Signup and view all the answers

What is the classification of the polynomial 5a³ - 4a - 6?

cubic trinomial Signup and view all the answers

What is the classification of the polynomial 4x² - 3x + 2x⁵ - 7 + 3x³?

quintic polynomial Signup and view all the answers

What is the degree of the monomial -12m²n²?

4 Signup and view all the answers

What is the classification of the number 12?

constant Signup and view all the answers

What is the degree of a monomial?

the sum of the exponents of all its variables Signup and view all the answers

What is the degree of a polynomial?

the highest degree of its terms Signup and view all the answers

What is a leading coefficient?

the coefficient of the first term when the polynomial is in standard form Signup and view all the answers

What is standard form of a polynomial?

a polynomial that is ordered from greatest degree to least degree Signup and view all the answers

What is the classification of the monomial 4x?

linear monomial Signup and view all the answers

Study Notes

Classifying Polynomials

Monomial: An expression consisting of a single term.
Binomial: An expression containing two distinct terms.
Trinomial: An expression made up of three individual terms.
Polynomial: Comprises one or more monomials, can be expressed as their sum or difference.
Constant: A polynomial with a degree of zero; it is a single numerical value.
Linear Polynomial: Defined by a degree of 1, indicated by a linear equation.
Quadratic Polynomial: Resides at degree 2, typically taking the form of a parabola.
Cubic Polynomial: Represents degree 3, often featuring inflection points in its graph.
Quartic Polynomial: Identified by a degree of 4, it can have up to four roots.
Quintic Polynomial: Denotes degree 5, can exhibit complex behaviors in graphs.
Nth Degree Polynomial: Any polynomial with a degree higher than 5; classified based on its highest degree term.
Degree of a Monomial: Obtained by summing the exponents of all variables present.
Degree of a Polynomial: Identified by the term with the highest degree within the polynomial.
Leading Coefficient: The coefficient associated with the polynomial's first term when in standard form.
Standard Form of a Polynomial: A conventional arrangement that lists terms in descending order of degree.
Examples:
- Monomial: 5a³b²c with a degree of 6 (3+2+1).
- Quadratic Binomial: 4x - 2x² with degree 2.
- Cubic Trinomial: 5a³ - 4a - 6 with degree 3.
- Quintic Polynomial: 4x² - 3x + 2x⁵ - 7 + 3x³ with a degree of 5.
- Quartic Monomial: -12m²n² with a degree of 4.
- Constant: The number 12 is a polynomial of degree zero.
Example Linear Monomial: 4x, characterized by a degree of 1.

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Test your knowledge on polynomials with these flashcards! Each card presents a key term related to polynomials, accompanied by its definition. Ideal for students looking to reinforce their understanding of algebraic expressions.