Classifying, Adding, Subtracting, and Multiplying 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. For example, 4x^2 + 3x - 5 is a polynomial.

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 3x^4 + 2x^2 - 5, the degree is 4.

Front

How do you classify polynomials based on the number of terms?

Back

Polynomials can be classified as: - Monomial: 1 term (e.g., 3x) - Binomial: 2 terms (e.g., x + 2) - Trinomial: 3 terms (e.g., x^2 + x + 1) - Polynomial: 4 or more terms.

Front

What is the result of subtracting two polynomials?

Back

To subtract polynomials, combine like terms by subtracting the coefficients of the same degree. For example, (2x^2 + 3x) - (x^2 + 2x) = (2x^2 - x^2) + (3x - 2x) = x^2 + x.

Front

What is the result of adding two polynomials?

Back

To add polynomials, combine like terms by adding the coefficients of the same degree. For example, (3x^2 + 2) + (4x^2 + 3) = (3x^2 + 4x^2) + (2 + 3) = 7x^2 + 5.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 5x^3 is a monomial.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 3x + 2 is a trinomial.

Front

How do you find the degree of a polynomial?

Back

To find the degree of a polynomial, identify the term with the highest exponent. For example, in -2x^2 - x^5 + 2x - 5, the degree is 5.

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. For example, in 4x^3 + 2x^2 - 5, the leading coefficient is 4.