Operations with Polynomials

Front

What is a polynomial?

Back

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

Front

What does it mean to simplify a polynomial?

Back

Simplifying a polynomial means to combine like terms and reduce the expression to its simplest form.

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 add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms.

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 polynomial.

Front

What is the area of a rectangle with length (x - 5) and width (3x + 1)?

Back

The area is found by multiplying length and width: A = (x - 5)(3x + 1) = 3x^2 - 14x - 5.

Front

What is the result of multiplying (4x + 1)(5x - 2)?

Back

The result is 20x^2 - 3x - 2.

Front

What is the process of multiplying polynomials?

Back

To multiply polynomials, use the distributive property or FOIL method for binomials.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 4x^3, 4 is the coefficient.