Monomial X Polynomial

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, 2xy).

Front

What is a polynomial?

Back

A polynomial is an expression that consists of variables raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication (e.g., 2x^2 + 3x - 5).

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 two or more terms inside parentheses.

Front

How do you simplify a monomial multiplied by a polynomial?

Back

To simplify a monomial multiplied by a polynomial, use the Distributive Property to multiply the monomial by each term in the polynomial.

Front

Simplify: 2x(-2x - 3)

Back

-4x^2 - 6x.

Front

Simplify: 4a(5a^2 - a + 4)

Back

20a^3 - 4a^2 + 16a.

Front

Simplify: (5p^9q^3)(2pq^7)

Back

10p^{10}q^{10}.

Front

Simplify: -2v(v - 5)

Back

-2v^2 + 10v.

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 - 5, 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 3x^2, 3 is the coefficient).