Classifying, Adding, Subtracting, 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, 2x^2 + 3x + 5 is a polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degree. For example, 2x^3 + 3x^2 + x + 5 is in standard form.

Front

How do you classify polynomials?

Back

Polynomials can be classified by their degree (e.g., linear, quadratic, cubic) and the number of terms (e.g., monomial, binomial, trinomial).

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 + 5, the degree is 3.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, such as 5x^2 or -3.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as 3x + 4 or x^2 - 5.

Front

What is a trinomial?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) and combine like terms. For example, (x + 2)(x + 3) = x^2 + 5x + 6.