Classifying, Adding, Subtracting, and Multiplying 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

True or False: The expression 5xy^-8 is a polynomial.

Back

False. Polynomials cannot have negative exponents.

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

Determine the degree of the polynomial -7xy^3z^2.

Back

The degree is 6 (3 from y^3 and 2 from z^2).

Front

What is a leading coefficient?

Back

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

Front

Determine the leading coefficient of the polynomial -8x - x^3 + 7x - 2.

Back

The leading coefficient is -1 (from the term -x^3).

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms to simplify the expression.

Front

Add the polynomials (x^3 + 6x - 5) and (-6x^2 + 4x + 3).

Back

The result is x^3 - 6x^2 + 10x - 2.

Front

What is the process of multiplying a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial.

Front

Multiply the polynomial -x^3 by (2x^3 - x^2 + 5).

Back

The result is -2x^6 + x^5 - 5x^3.