Operations with Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, 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 polynomial. For example, in the polynomial 5x^3 - 2x^2 + 4, the degree is 3.

Front

How do you classify polynomials by degree?

Back

Polynomials can be classified as follows: 0 degree (constant), 1 degree (linear), 2 degree (quadratic), 3 degree (cubic), and so on.

Front

What is the result of multiplying two binomials?

Back

The result of multiplying two binomials is a polynomial, which can be found using the distributive property or the FOIL method (First, Outside, Inside, Last).

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 does it mean to simplify an expression?

Back

To simplify an expression means to combine like terms and reduce it to its simplest form, making it easier to understand or solve.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to each term of the polynomial being subtracted, and then combine like terms.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum or difference.

Front

What is the result of (a + b)(c + d)?

Back

The result of (a + b)(c + d) is ac + ad + bc + bd, obtained by applying the distributive property.