Problem 13 - Beginning and Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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 1: Identify the polynomial in one variable

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

Step 2: 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: \(3x^4, -2x^3, 7x^2, -x\).

Step 3: 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.