CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. The polynomial 2x⁵ - x + 4 is a trinomial of degree _________.

Verified step by step guidance

1. Identify the degree of the polynomial by looking at the term with the highest exponent. The degree of a polynomial is the highest power of the variable in the expression.
2. In the polynomial \$2x^{5} - x + 4\(, observe the exponents of each term: \(5\) in \)2x^{5}\(, \(1\) in \)-x$, and \(0\) in the constant term \(4\).
3. Since the highest exponent is \(5\), the degree of the polynomial is \(5\).
4. Note that the polynomial has three terms: \$2x^{5}\(, \)-x$, and \(4\), which makes it a trinomial (a polynomial with exactly three terms).
5. Therefore, the polynomial \$2x^{5} - x + 4$ is a trinomial of degree \(5\).

Key Concepts

Polynomial Degree

The degree of a polynomial is the highest power of the variable in the expression. It indicates the polynomial's order and helps determine its behavior and graph shape. For example, in 2x⁵ - x + 4, the highest exponent is 5, so the degree is 5.

Polynomial Terms

A polynomial consists of terms separated by plus or minus signs. Each term includes a coefficient and a variable raised to a non-negative integer exponent. The number of terms defines if it is a monomial, binomial, trinomial, etc. Here, 2x⁵ - x + 4 has three terms, making it a trinomial.

Trinomial Definition

A trinomial is a polynomial with exactly three terms. These terms can have different degrees and coefficients. Recognizing the number of terms helps classify polynomials and understand their structure, which is essential for operations like factoring or graphing.