Multiplying Polynomials

Front

What is the distributive property in algebra?

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, distribute the monomial to each term of the polynomial.

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax^2 + bx + c.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degree.

Front

What is a generic rectangle used for in polynomial multiplication?

Back

A generic rectangle is a visual tool used to organize the multiplication of polynomials, helping to keep track of terms.

Front

How do you combine like terms in a polynomial?

Back

To combine like terms, add or subtract the coefficients of terms that have the same variable raised to the same power.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials.

Front

What is the result of multiplying (x - 8)(x + 6)?

Back

The result is x^2 - 2x - 48.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree and determines the polynomial's end behavior.

Front

What is the process of using a generic rectangle to multiply (2x)(2x - 3)?

Back

Draw a rectangle, label one side with 2x and the other with (2x - 3), then fill in the rectangle to find the product: 4x^2 - 6x.