Monomials and Polynomials

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables (e.g., 3x^2, -4xy, 7).

Front

What is a polynomial?

Back

A polynomial is an expression that consists of variables raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication (e.g., 2x^3 + 3x^2 - x + 5).

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

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) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

Front

What is a like term?

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, while 3x^2 and 4x are not.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial has only one term, while a polynomial can have multiple terms. For example, 5x is a monomial, while 2x^2 + 3x - 4 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 degrees. For example, 4x^3 + 2x^2 - x + 5 is in standard form.

Front

How do you find the degree of a monomial?

Back

To find the degree of a monomial, add the exponents of all the variables in the term. For example, the degree of -4xy^4 is 1 + 4 = 5.

Front

What is the sum of (2x^2 + 5x - 7) and (3 - 4x^2 + 6x)?

Back

The sum is -2x^2 + 11x - 4.