Polynomials and Polynomial Functions

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 + 1 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

What does it mean to factor a polynomial?

Back

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

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF of a set of terms is the largest factor that divides all the terms. For example, the GCF of 6m^2 and 16m is 2m.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a^2 - b^2 = (a - b)(a + b). For example, x^2 - 16 can be factored as (x - 4)(x + 4).

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors. For example, in x^3 - 4x^2 - 4x + 16, we can group as (x^3 - 4x^2) + (-4x + 16).

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 + 5x + 6 is a trinomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 2x^3 + 3x^2 - x + 5 is in standard form.

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 - 3)(x + 2) = 0, then x = 3 or x = -2.