Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, 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 - x + 5, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = (2 + 4)x^2 + 3x + 5 = 6x^2 + 3x + 5.

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 + 2) - (x^2 + 4) = (3 - 1)x^2 + (2 - 4) = 2x^2 - 2.

Front

What are like terms in polynomials?

Back

Like terms are terms 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 expression?

Back

Simplifying a polynomial expression involves combining like terms and arranging the terms in descending order of their degrees.

Front

What is the result of adding (x + 2x^2) and (4x^2 + 7x)?

Back

The result is 6x^2 + 8x.

Front

What is the result of subtracting (4n^4 - 8n + 4) from (8n^2 + 4n^4 + 1)?

Back

The result is -8n^2 - 8n + 3.

Front

How do you identify the leading coefficient of a polynomial?

Back

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

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, from highest to lowest.