Polynomial Operations

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 are the degrees of polynomials?

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

What is the sum of two polynomials?

Back

The sum of two polynomials is obtained by adding their corresponding coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property or the FOIL method. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the difference between two polynomials?

Back

The difference between two polynomials is found by subtracting the corresponding coefficients. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degrees of its terms. For example, 4x^3 + 2x^2 - x + 5 is in standard form.

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, the leading coefficient is 3.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property to multiply each term in one polynomial by each term in the other polynomial.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 5x + 6 is a trinomial.