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 by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 4) = (5x^2 - 2x^2) + (3 - 4) = 3x^2 - 1.

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, 2x^2 + 3x - 4 + x^2 simplifies to 3x^2 + 3x - 4.

Front

What is the distributive property in relation to polynomials?

Back

The distributive property states that a(b + c) = ab + ac. This property is used to multiply a term by a polynomial. For example, 2(x + 3) = 2x + 6.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property or the FOIL method for binomials. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

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.