Classifying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. It classifies polynomials as constant (degree 0), linear (degree 1), quadratic (degree 2), cubic (degree 3), quartic (degree 4), quintic (degree 5), and so on.

Front

How do you classify a polynomial by degree?

Back

To classify a polynomial by degree, identify the term with the highest exponent of the variable. The degree of that term determines the classification.

Front

What is a leading coefficient?

Back

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables.

Front

What is a linear polynomial?

Back

A linear polynomial is a polynomial of degree 1, which can be expressed in the form ax + b, where a and b are constants.

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, which can be expressed in the form ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is a cubic polynomial?

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A cubic polynomial is a polynomial of degree 3, which can be expressed in the form ax³ + bx² + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What is the difference between a polynomial and a monomial?

Back

A polynomial can have multiple terms, while a monomial consists of only one term.

Front

What is the standard form of a polynomial?

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The standard form of a polynomial is when the terms are arranged in descending order of their degrees.