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 expression?

Back

Simplifying a polynomial expression 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 sum.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c). It is faster than long division.

Front

What is the degree of a polynomial?

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 leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last.