Part III: For each polynomial, determine the degree and write the polynomial in descending order.

Question

A. –4x2 – 12 + 11x4

-12 –4x2 + 11x4, degree 1

11x4 –4x2 -12, degree 4

–4x2 – 12 + 11x4, degree 2

11x4 –12-4x2, degree 4

Answer 1

To determine the degree of the polynomial and write it in descending order, we'll first rearrange the terms in decreasing order of their exponents.

The given polynomial is:
\(-4x^2 - 12 + 11x^4\).

1. Identify the highest power of \(x\):

   • The term \(11x^4\) has the highest power, which is 4. This means the degree of the polynomial is 4.

2. Rewrite the polynomial in descending order:

   • Start with the term with the highest degree first.
   • So, it will be \(11x^4 - 4x^2 - 12\).

The resulting polynomial in descending order is:
\(11x^4 - 4x^2 - 12\)

The degree of the polynomial is:
Degree 4

So the correct option is:
11x4 - 4x2 - 12, degree 4.