Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

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

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 the polynomial 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8) = (1y^3 + 2y^3) + (3y^2 + 4y^2) + (-4y) + (3) = 3y^3 + 7y^2 - 4y + 3.

Front

What is the process of multiplying polynomials?

Back

To multiply polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Front

What is a binomial?

Back

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

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms. For example, x^2 + 3x + 2 is a trinomial.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have one or more terms. For example, 4x is a monomial, while 4x + 3 is a polynomial.

Front

What is the zero polynomial?

Back

The zero polynomial is the polynomial that has all coefficients equal to zero. It is represented as 0 and has no degree.

Front

What does it mean to factor a polynomial?

Back

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