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 the polynomials in the expression (-x^3 + 7x^4) + (-6x^3 + 5x^4)?

Back

The degrees of the polynomials are 4 (from 7x^4) and 3 (from -x^3 and -6x^3). The resulting polynomial has a degree of 4.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable part the same.

Front

What are like terms in a polynomial?

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.

Front

What is the result of adding the polynomials (-7x^3 - 2x^4) and (4x^3 + 4x^4)?

Back

The result is 2x^4 - 3x^3.

Front

What is the process for subtracting polynomials?

Back

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

Front

What is the degree of the polynomial 6v^4 + v^3 - 8v^2 - 1?

Back

The degree of the polynomial is 4, which is the highest power of the variable v.

Front

What is the result of the expression (6 + 7k^3 + k^2) + (-5k^3 + k^2 + 3)?

Back

The result is 2k^3 + 2k^2 + 9.

Front

What does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of their degrees.

Front

What is the result of subtracting the polynomials (-3p^2 - 8p^4) and (-3p^2 - 6p^4)?

Back

The result is -2p^4.