Multiplying Monomials and 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 raised to non-negative integer powers.

Front

What is a polynomial?

Back

A polynomial is an expression that consists of variables raised to whole number powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

How do you multiply a monomial by a polynomial?

Back

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

Front

What is the result of multiplying x^3(2x^2 + 3x)?

Back

The result is 2x^5 + 3x^4.

Front

What is the result of multiplying 10(x + y + z)?

Back

The result is 10x + 10y + 10z.

Front

How do you simplify 10x(2x^2 + 3x + 4)?

Back

The simplification results in 20x^3 + 30x^2 + 40x.

Front

What is the result of multiplying 3x^3(2x^2 + 9x + 6)?

Back

The result is 6x^5 + 27x^4 + 18x^3.

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

What is a coefficient in a polynomial?

Back

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