Exponent Rules & 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. For example, in the polynomial 4x^3 + 2x^2 + 5, the degree is 3.

Front

How do you classify a polynomial based on its degree?

Back

Polynomials are classified as follows: 0 degree - Constant, 1 degree - Linear, 2 degrees - Quadratic, 3 degrees - Cubic, 4 degrees - Quartic, 5 degrees - Quintic, and so on.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, such as 3x or -5y^2.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as x + 2 or 3x^2 - 4.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms, such as x^2 + 3x + 2.

Front

How do you identify the leading coefficient of a polynomial?

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The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 5.

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, from highest to lowest.

Front

What is the difference between a polynomial and a rational expression?

Back

A polynomial is an expression that consists only of non-negative integer powers of variables, while a rational expression is a ratio of two polynomials.

Front

What is the significance of the degree of a polynomial in graphing?

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The degree of a polynomial affects the shape and number of turns in its graph. Higher degree polynomials can have more complex shapes.