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Chapter 0: Problem 8

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

Short Answer

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

Step by step solution

01

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 \(x^0\).
02

Identify the Exponents of Each Term

The exponents of \(x\) in the polynomial terms are \(2\), \(3\), \(4\), and \(0\) respectively.
03

Find the Maximum Exponent

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

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