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^2 + 9x + 6)

Back

6x^3 + 27x^2 + 18x

Front

What is the degree of a polynomial?

Back

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

Front

How do you combine like terms?

Back

You combine like terms by adding or subtracting the coefficients of terms that have the same variable raised to the same power.

Front

What is a coefficient in a polynomial?

Back

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

Front

Multiply: 4x(3x^3 + 2x^2 + 5)

Back

12x^4 + 8x^3 + 20x

Front

What is the result of multiplying a monomial by a polynomial?

Back

The result is a new polynomial formed by distributing the monomial across each term of the polynomial.