9.4 Multiplying Monomials and Polynomials HW

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^2, -5, 7xy).

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^3 + 3x^2 - x + 5).

Front

How do you multiply two monomials?

Back

To multiply two monomials, multiply their coefficients and add their exponents for like bases (e.g., (4x)(2x^2) = 8x^(1+2) = 8x^3).

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 inside a parenthesis.

Front

Simplify: (3x)(4x^2)

Back

12x^3.

Front

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

Back

Multiply the monomial by each term of the polynomial separately and combine like terms.

Front

Simplify: -2x(3x + 4)

Back

-6x^2 - 8x.

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 - x, the degree is 3).

Front

Simplify: 5(2x + 3)

Back

10x + 15.

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).