Multiplying Polynomials by Monomials

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 (e.g., 3x, -5, 7xy).

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 (e.g., 2x^2 + 3x + 5).

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 and combine like terms if necessary.

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

Multiply: -2x(5x^2 + 8)

Back

-10x^3 - 16x.

Front

Multiply: -2x(x^7 + 5)

Back

-2x^8 - 10x.

Front

Multiply: 5x(4x^3 + 8)

Back

20x^4 + 40x.

Front

Multiply: -5x^3(2x^2 - 6x + 8)

Back

-10x^5 + 30x^4 - 40x^3.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial (e.g., in 4x^2, 4 is the coefficient).