8-7 Multiplying Polynomials B

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 two binomials?

Back

To multiply two binomials, use the FOIL method: First, Outer, Inner, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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 binomial?

Back

A binomial is a polynomial with exactly two terms, such as (x + 3) or (2n - 5).

Front

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

Back

The result is x^2 + 8x + 15.

Front

What is the result of multiplying (2n - 3)(n + 4)?

Back

The result is 2n^2 + 5n - 12.

Front

What is the result of multiplying (x + 3)(2x^2 - 4x + 8)?

Back

The result is 2x^3 + 2x^2 - 4x + 24.

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 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.