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 degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 2x^2 - x + 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) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

Front

What are like terms in polynomials?

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 process of simplifying a polynomial?

Back

Simplifying a polynomial involves combining like terms and reducing the expression to its simplest form. For example, 3x + 2x - 5 simplifies to 5x - 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3x) - (2x^2 + 4) = (5x^2 - 2x^2) + 3x - 4 = 3x^2 + 3x - 4.

Front

What is the product of two polynomials?

Back

The product of two polynomials is found by using the distributive property (also known as the FOIL method for binomials). For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, such as 3x^2. A polynomial can have multiple terms, such as 2x^2 + 3x - 5.

Front

What is the factorization of a polynomial?

Back

Factorization of 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 zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero. For example, if (x - 2)(x + 3) = 0, then x - 2 = 0 or x + 3 = 0.