Multiplying Monomials and 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 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 distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term in a sum.

Front

What is the result of multiplying 10x by (2x^2 + 3x + 4)?

Back

The result is 20x^3 + 30x^2 + 40x.

Front

What is the result of multiplying 2x^2 by (x + 5)?

Back

The result is 2x^3 + 10x^2.

Front

What is the result of multiplying x by (x + 4)?

Back

The result is x^2 + 4x.

Front

How do you multiply two monomials?

Back

To multiply two monomials, multiply their coefficients and add their exponents for like bases.

Front

What is the result of multiplying 4m by (3m^7 + 2m^5)?

Back

The result is 12m^8 + 8m^6.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial, which determines its behavior and the number of roots it can have.