12/3/24 Intro to 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, 2x^3 + 3x^2 - x + 5 is a polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their exponents. For example, 2x^3 + 3x^2 + x + 5 is in standard form.

Front

How do you simplify the expression 2x + 1 + 7x?

Back

Combine like terms: 2x + 7x + 1 = 9x + 1.

Front

What is a constant in a polynomial?

Back

A constant is a term in a polynomial that does not contain any variables. For example, in the polynomial 5x^3 + 2, the constant is 2.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 4x^2 is a monomial.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 5 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 2x + 1 is a trinomial.

Front

How do you classify the polynomial 2x^4 + 14x^3 - 2x^2?

Back

It is classified as a trinomial because it has three terms.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of its variable. For example, in 4x^3 + 2x^2 + 5, the degree is 3.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree. For example, in 3x^4 + 2x^3, the leading coefficient is 3.