Problem 6 - College Algebra

Question

Find the degree of the polynomial. $$-4 x^{3}+7 x^{2}-11$$

Step-by-Step Solution

Answer

The degree of the polynomial \(-4x^3+7x^2-11\) is 3.

Step 1: Identify the terms of the polynomial

A polynomial can be written as the sum of several terms. In this case, the polynomial is \(-4x^3+7x^2-11\) , the terms are \(-4x^3\), \(7x^2\), and \(-11\).

Step 2: Find the powers of x in each term

Look at each term individually to determine the power of x. In the term \(-4x^3\), the power of x is 3. In the term \(7x^2\), the power of x is 2. The term \(-11\) does not contain the variable x, so it will be counted as power 0.

Step 3: Determine the degree of the polynomial

The degree of the polynomial is the highest power of x. Here, comparing the powers of x, we can see that the highest power is 3. So, the degree of the polynomial \(-4x^3+7x^2-11\) is 3.