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

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining 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 and exponent. For example, 3x^2 and 5x^2 are like terms.

Front

How do you subtract polynomials?

Back

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

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 coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 7x^2, 7 is the coefficient.

Front

What is the constant term in a polynomial?

Back

The constant term is the term in a polynomial that does not contain any variables. For example, in 3x^2 + 4x + 5, the constant term is 5.

Front

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

Back

Combine like terms: (2x^2 + 4x^2) + (3 + 5) = 6x^2 + 8.

Front

What is the result of adding (-x^3 + 7x^4) + (-6x^3 + 5x^4)?

Back

The result is 12x^4 - 7x^3.

Front

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

Back

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