Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 4x^3 + 2x^2 - x, the degree is 3.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 3x^4 + 2x^3 - x + 5.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

What is the product of a polynomial and a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, 3x(2x^2 + 4x) = 6x^3 + 12x^2.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It is used to multiply a single term by a sum or difference.

Front

How do you factor a polynomial?

Back

Factoring a polynomial involves expressing it as a product of its factors. For example, x^2 - 9 can be factored as (x - 3)(x + 3).

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 5x is a monomial, while 5x + 3 is a polynomial.

Front

What is the FOIL method?

Back

The FOIL method is a technique for multiplying two binomials. It stands for First, Outside, Inside, Last. For example, (x + 2)(x + 3) = x^2 + 5x + 6.