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Chapter 6: Problem 13

How do you determine the degree of a polynomial in one variable?

Short Answer

Expert verified
To determine the degree of a polynomial in one variable, identify the highest exponent of the variable present in the polynomial. For example, in the polynomial \(P(x) = 3x^4 - 2x^3 + 7x^2 - x + 6\), the highest exponent is 4, so the degree is 4.

Step by step solution

01

Identify the polynomial in one variable

For this explanation, let's consider the given polynomial: \(P(x) = 3x^4 - 2x^3 + 7x^2 - x + 6\).
02

Examine the exponents of the variable

In our example, the polynomial has the following exponents: 4, 3, 2, and 1. These exponents correspond to the given terms: \(3x^4, -2x^3, 7x^2, -x\).
03

Determine the highest exponent

Among the exponents, 4 is the highest. Therefore, the degree of the given polynomial \(P(x) = 3x^4 - 2x^3 + 7x^2 - x + 6\) is 4. So, to determine the degree of a polynomial in one variable, simply identify the highest exponent of the variable present in the polynomial.

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Most popular questions from this chapter

Find the following special products. $$(z+4)(z-4)$$

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