Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 2x and 3x are like terms, while 2x and 2y are not.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x + 3) + (4x + 5) = (2x + 4x) + (3 + 5) = 6x + 8.

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 + 4) - (2x + 5) = (3x - 2x) + (4 - 5) = x - 1.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 4x^3 + 2x^2 + 5, the degree is 3.

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 5x^4 + 3x^2 + 2, the leading coefficient is 5.

Front

What is the result of (3x + 2) + (4x - 5)?

Back

The result is 7x - 3.

Front

What is the result of (5x^2 + 3x) - (2x^2 + x)?

Back

The result is 3x^2 + 2x.

Front

What are the steps to simplify the expression (2x + 3) + (3x - 4)?

Back

Combine like terms: (2x + 3x) + (3 - 4) = 5x - 1.

Front

What is the result of (x^2 + 2x + 1) - (x^2 - x)?

Back

The result is 3x + 1.