Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. 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

What is the product of (x + 2)(x + 3)?

Back

The product is x^2 + 5x + 6.

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. For example, 3x * (x^2 + 2x + 1) = 3x^3 + 6x^2 + 3x.

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 product of (2x + 1)(3x + 4)?

Back

The product is 6x^2 + 11x + 4.

Front

What is the FOIL method?

Back

The FOIL method is a technique for multiplying two binomials. It stands for First, Outside, Inside, Last, referring to the order in which you multiply the terms.

Front

What is the product of (x + 1)(x - 1)?

Back

The product is x^2 - 1.

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms, such as x^2 + 5x + 6.