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Chapter 5: Problem 111

What is the degree of a polynomial? Provide an example with your explanation.

Short Answer

Expert verified
The degree of a polynomial is the highest power of the variable in the polynomial, also represented by the largest exponent of that variable. For instance, in the polynomial \(5x^4 - 2x^2 + 3x + 7\), the degree is 4.

Step by step solution

01

Define the Degree of a Polynomial

The degree of a polynomial is the highest power of the variable in the polynomial. It is the same as the greatest exponent of that variable.
02

Recognizing the Degree in a Polynomial

When looking at a polynomial, the term with the highest power represents the degree of the polynomial. For instance, if we have a polynomial \(2x^3 + 4x^2 + 7x + 5\), the degree of this polynomial is 3, because the largest exponent in this polynomial is 3.
03

Giving an Example of Degree of a Polynomial

For example, consider the polynomial \(P(x) = 5x^4 - 2x^2 + 3x + 7\). In this case, the highest power of x is 4, so the degree of the polynomial is 4.

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Most popular questions from this chapter

Explain the difference between performing these two operations: $$2 x^{2}+3 x^{2} \text { and }\left(2 x^{2}\right)\left(3 x^{2}\right)$$

Use a vertical format to find each product. $$\begin{aligned}&4 z^{3}-2 z^{2}+5 z-4\\\&3 z-2\end{aligned}$$

Graph \(3 x-2 y=6\) using intercepts. (Section 3.2 Example 4 )

Explain how to find any nonzero number to the 0 power.

Use a vertical format to find each product. $$\begin{array}{r} 9 y^{3}-7 y^{2}+5 y \\ 3 y^{2}+5 y \\ \hline \end{array}$$
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