Problem 8 - College Algebra Essentials

Question

Find the degree of the polynomial. $$x^{2}-8 x^{3}+15 x^{4}+91$$

Step-by-Step Solution

Answer

The degree of the polynomial \(x^{2}-8x^{3}+15x^{4}+91\) is 4.

Step 1: Identify the terms of the polynomial

Identify each term in the polynomial. Terms are separated by a '+' or '-' sign. In the polynomial \(x^{2}-8x^{3}+15x^{4}+91\), the terms are \(x^{2}, -8x^{3}, 15x^{4},\) and \(91\).

Step 2: Find the Degree of Each Term

Identify the exponential value for each term, this is the degree of that particular term. The degree of \(x^{2}\) is 2, the degree of \(-8x^{3}\) is 3, the degree of \(15x^{4}\) is 4, and the term \(91\) has a degree of 0 (since it's a constant).

Step 3: Identify the Highest Degree

The degree of the polynomial is equal to the highest degree of its terms. In this case, the degree is 4, as that's the highest degree found in step 2.