Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication. For example, 3x^2 + 2x - 5 is a polynomial.

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 - x + 7, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. Like terms are terms that have the same variable raised to the same power. For example, (3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 5.

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Front

What is the process of simplifying a polynomial?

Back

Simplifying a polynomial involves combining like terms and removing any parentheses. For example, to simplify 2x + 3x - 5, combine like terms to get 5x - 5.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term (e.g., 3x), a binomial has two terms (e.g., 3x + 2), and a trinomial has three terms (e.g., 3x^2 + 2x + 1).

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x^2 + 2x) - (x^2 + 4) = 2x^2 + 2x - 4.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 + 2x^2 - x + 5 is in standard form.

Front

What is the leading coefficient of a polynomial?

Back

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

Front

What is the zero polynomial?

Back

The zero polynomial is a polynomial in which all coefficients are zero. It is represented as 0 and has no degree.