https://file.aiquickdraw.com/mathbot/file/1725503509873b0nyzkza.jpg

The image shows an algebraic expression, and you're being asked to determine the degree of the resulting polynomial.

Let's break down the expression:

\[
(8x^3 + 18x^2 - 11) - (2x^3 + x^2 - x + 2)
\]

First, distribute the negative sign through the second polynomial:

\[
8x^3 + 18x^2 - 11 - 2x^3 - x^2 + x - 2
\]

Next, combine like terms:

\[
(8x^3 - 2x^3) + (18x^2 - x^2) + x + (-11 - 2)
\]

Simplify each term:

\[
6x^3 + 17x^2 + x - 13
\]

The degree of a polynomial is the highest power of the variable \( x \) in the expression. In this case, the highest power is 3 (from \( 6x^3 \)). 

So, the degree of the resulting polynomial is **3**.

Would you like further details on this problem, or do you have any additional questions?

Here are some related questions that you might find helpful:
1. What is a polynomial, and how is it structured?
2. How do you add and subtract polynomials?
3. What does the degree of a polynomial tell you about its graph?
4. How do you multiply polynomials?
5. How can you factor polynomials?

**Tip:** When combining polynomials, always align like terms (terms with the same power of the variable) to simplify the process.

(8x^3 + 18x^2 - 11) - (2x^3 + x^2 - x + 2) = ?

Learn how to subtract two polynomials and find the degree of the resulting polynomial expression (8x^3 + 18x^2 - 11) - (2x^3 + x^2 - x + 2). This step-by-step solution covers combining like terms and understanding the degree of polynomials, suitable for students in Grades 9-10.

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