Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to multiply each term in one polynomial by each term in another polynomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term in a polynomial.

Front

How do you multiply a monomial by a polynomial?

Back

To multiply a monomial by a polynomial, multiply the monomial by each term in the polynomial and combine like terms.

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as x + 5 or 3x^2 - 2.

Front

What is the result of multiplying (x - 3)(x + 10)?

Back

The result is x^2 + 7x - 30.

Front

What is the result of multiplying 5(3x + 2)?

Back

The result is 15x + 10.

Front

What is the process of combining like terms?

Back

Combining like terms involves adding or subtracting 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 polynomial. For example, in 4x^3 + 2x^2 - x, 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. For example, in 5x^2, 5 is the coefficient.