Multiplying Monomial by 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 (e.g., 3x, -5, 7a^2b).

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 + 1).

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

Simplify: 3a(5a^2 + 8a + 2)

Back

15a^3 + 24a^2 + 6a.

Front

What is the result of multiplying -5x^6 by (3x^2 - 12x + 30)?

Back

-15x^8 + 60x^7 - 150x^6.

Front

What does it mean to combine like terms?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression (e.g., in 4x^3 + 2x^2, the degree is 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 5x^2, 5 is the coefficient).

Front

What is the difference between a monomial and a binomial?

Back

A monomial has one term, while a binomial has two terms (e.g., 3x is a monomial; 3x + 2 is a binomial).