Multiplying a 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

What does it mean to multiply a polynomial by a monomial?

Back

Multiplying a polynomial by a monomial involves distributing the monomial to each term of the polynomial.

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

Simplify: x(3x^2 + 5x - 2)

Back

3x^3 + 5x^2 - 2x

Front

Multiply: 4y(2y^3 + 3y^2 + y)

Back

8y^4 + 12y^3 + 4y^2

Front

What is the degree of a polynomial?

Back

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

Front

Multiply: 5m(3m^2 + 2m + 1)

Back

15m^3 + 10m^2 + 5m

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial.