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

What does it mean to combine like terms in a polynomial?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power. For example, in 3x + 2x, you can combine to get 5x.

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

Front

How do you simplify the expression (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

To simplify, combine like terms: (4n^4 - 4n^4) - 8n^2 - 8n + (4 - 1) = -8n^2 - 8n + 3.

Front

What is the result of adding the polynomials (4v^3 + 3v - 8v^4) + (4v - 8v^4 - 7)?

Back

The result is -16v^4 + 4v^3 + 7v - 7.

Front

What is a monomial?

Back

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

Front

What is the product of a monomial and a polynomial?

Back

To find the product, multiply the monomial by each term in the polynomial. For example, -x^3(2x^3 - x^2 + 5) = -2x^6 + x^5 - 5x^3.

Front

What does it mean for polynomials to be in standard form?

Back

Polynomials are in standard form when their terms are arranged in descending order of their degrees. For example, 3x^4 + 2x^3 - x + 5 is in standard form.

Front

How do you subtract polynomials?

Back

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

Front

What are coefficients in a polynomial?

Back

Coefficients are the numerical factors in front of the variables in a polynomial. For example, in 4x^3, 4 is the coefficient.