Multiply Polynomial by a Monomial

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.

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 exponents.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial, multiplying the coefficients and adding the exponents of like bases.

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 or difference.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What happens to the exponents when multiplying like bases?

Back

When multiplying like bases, you add the exponents together.

Front

Can a polynomial have negative exponents?

Back

No, a polynomial cannot have negative exponents; all exponents must be non-negative integers.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial, representing how many times the variable is multiplied.

Front

What is the result of multiplying 3x^2 by 2x?

Back

The result is 6x^3, obtained by multiplying the coefficients (3 and 2) and adding the exponents (2 and 1).

Front

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

Back

The result is 3x + 6, obtained by distributing 3 to both terms in the polynomial.