Multiply Polynomial by a Monomial

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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.

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

Multiply: 3x * (2x + 4)

Back

6x^2 + 12x

Front

Multiply: 5y * (3y^2 + 2y - 1)

Back

15y^3 + 10y^2 - 5y

Front

What happens to the exponents when multiplying like bases?

Back

When multiplying like bases, you add the exponents together.

Front

Multiply: 4a * (a^2 + 3a + 5)

Back

4a^3 + 12a^2 + 20a

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of its variable(s) in the expression.

Front

Multiply: -2m * (m^3 - 4m^2 + 2)

Back

-2m^4 + 8m^3 - 4m