In Exercises 5–8, find the degree of the polynomial. 3x^2−5x+4

Verified step by step guidance

1. Identify each term in the polynomial: \(3x^2\), \(-5x\), and \(4\).
2. Determine the degree of each term by looking at the exponent of the variable \(x\).
3. The term \(3x^2\) has a degree of 2, \(-5x\) has a degree of 1, and \(4\) has a degree of 0.
4. The degree of the polynomial is the highest degree of its terms.
5. Compare the degrees of the terms: 2, 1, and 0. The highest degree is 2.

Key Concepts

Polynomial Degree

The degree of a polynomial is the highest power of the variable in the polynomial expression. For example, in the polynomial 3x^2−5x+4, the term with the highest exponent is 3x^2, which has a degree of 2. This concept is crucial for classifying polynomials and understanding their behavior.

Polynomial Terms

A polynomial consists of one or more terms, each of which is a product of a coefficient and a variable raised to a non-negative integer exponent. In the expression 3x^2−5x+4, the terms are 3x^2, -5x, and 4. Recognizing these terms helps in identifying the degree and other properties of the polynomial.

Coefficients

Coefficients are the numerical factors in each term of a polynomial. In the polynomial 3x^2−5x+4, the coefficients are 3 for the x^2 term, -5 for the x term, and 4 for the constant term. Understanding coefficients is essential for performing operations on polynomials and analyzing their characteristics.