Adding/subtracting and Multiplying monomials x polynomials

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers.

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of one or more terms, where each term is a product of a constant and a variable raised to a non-negative integer power.

Front

How do you add polynomials?

Back

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

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. Only the coefficients of like terms can be added or subtracted.

Front

What is the process for subtracting polynomials?

Back

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

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum or difference.

Front

How do you multiply a monomial by a polynomial?

Back

To multiply a monomial by a polynomial, distribute the monomial to each term of the polynomial, multiplying the coefficients and adding the exponents of like bases.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial, representing how many times the variable is multiplied.

Front

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

Back

The result is 7x^2 + 7x, combining like terms.