Problem 8 - College Algebra

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 given polynomial \(x^2 - 8x^3 + 15x^4 + 91\) is \(4\).

Step 1: Identify the Terms of the Polynomial

The terms of the polynomial \(x^2-8x^3+15x^4+91\) are \(x^2\), \(-8x^3\), \(15x^4\), and \(91\). Notice that 91 has an implicit \(x^0\).

Step 2: Identify the Exponents of Each Term

The exponents of \(x\) in the polynomial terms are \(2\), \(3\), \(4\), and \(0\) respectively.

Step 3: Find the Maximum Exponent

The largest exponent among those identified in Step 2 is \(4\), and thus the degree of the polynomial is \(4\).