Operations with 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 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 - 7, the degree is 3.

Front

How do you add polynomials?

Back

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

Front

What is the process of subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^2 + 4) - (2x^2 + 1) = x^2 + 3.

Front

What does it mean to multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to multiply each term in one polynomial by each term in the other. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is a binomial?

Back

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

Front

What is a trinomial?

Back

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

Front

How do you factor a polynomial?

Back

Factoring a polynomial involves expressing it as a product of its factors. For example, x^2 - 9 can be factored as (x - 3)(x + 3).

Front

What is the difference between a coefficient and a variable?

Back

A coefficient is a numerical factor in a term of a polynomial, while a variable is a symbol that represents an unknown value. For example, in 5x^2, 5 is the coefficient and x is the variable.

Front

What are like terms?

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.