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 a polynomial by looking at the highest power of the variable present in the expression.
2. In the polynomial \(2x^5 - x + 4\), the term with the highest power of \(x\) is \(2x^5\).
3. The degree of the polynomial is determined by the exponent of this term, which is 5.
4. Therefore, the polynomial \(2x^5 - x + 4\) is of degree 5.
5. Fill in the blank with the number 5 to complete the sentence.

Key Concepts

Polynomial Degree

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 2x⁵ - x + 4, the term with the highest exponent is 2x⁵, which has a degree of 5. Understanding the degree is crucial as it determines the polynomial's behavior and the number of roots it can have.

Trinomial Definition

A trinomial is a polynomial that consists of exactly three terms. In the expression 2x⁵ - x + 4, there are three distinct terms: 2x⁵, -x, and 4. Recognizing the structure of polynomials helps in classifying them and understanding their properties.

Polynomial Classification

Polynomials can be classified based on their number of terms (monomial, binomial, trinomial) and their degree. The polynomial in question is classified as a trinomial due to its three terms, but it is important to note that its degree is determined solely by the term with the highest exponent, which is 5 in this case.