Adding and Subtracting 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. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

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

How do you subtract polynomials?

Back

Subtracting polynomials involves distributing the negative sign to the second polynomial and then combining like terms. For example, (3x^2 + 2x) - (x^2 + 4) = (3x^2 - x^2) + 2x - 4 = 2x^2 + 2x - 4.

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 the polynomial 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

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable and exponent. For example, 3x + 4x = 7x.

Front

What is the result of adding (2x^2 + 3x) and (3x^2 + 4)?

Back

The result is 5x^2 + 3x + 4.

Front

What is the result of subtracting (5x^2 + 2x) from (3x^2 + 4)?

Back

The result is -2x^2 + 2x + 4.

Front

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

Back

The sum is 3x^2 + x + 2.