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, 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 polynomial. 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, which are terms that have the same variable raised to the same power.

Front

What are like terms in polynomials?

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.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the terms of the polynomial being subtracted, and then combine like terms.

Front

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

Back

The result is 3a^2 + 2a.

Front

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

Back

The result is 2x^3 - 6x.

Front

What is the importance of the distributive property in polynomial operations?

Back

The distributive property allows you to multiply a single term by each term in a polynomial, which is essential for both addition and subtraction of polynomials.

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

How do you combine the polynomials (2x^2 + 3x) and (4x^2 - 5)?

Back

Combine like terms to get 6x^2 + 3x - 5.