Multiplying Polynomials

Front

What is a polynomial?

Back

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

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, which can be expressed in the standard form as ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to combine like terms. Each term in the first polynomial is multiplied by each term in the second 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 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 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. For example, 4x^3 + 2x^2 - x + 5.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 3x^2, 3 is the coefficient.

Front

What is a term in a polynomial?

Back

A term in a polynomial is a single mathematical expression that can be a constant, a variable, or a product of both. For example, 5x^2 is a term.

Front

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

Back

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

Front

What is the result of multiplying (2x - 1)(x + 4)?

Back

The result is 2x^2 + 7x - 4.