The image you have provided shows a polynomial long division problem. The expression inside the division bracket appears to be a polynomial:

$2x^5 - x^4 + 0x^3 - 0x^2 - 2x + 1$

It is being divided by $x - 2$.

Here's how to approach polynomial long division:

1. Divide the first term: Divide $2x^5$ by $x$. This gives $2x^4$.

2. Multiply: Multiply $2x^4$ by $x - 2$, which gives: $(2x^4)(x - 2) = 2x^5 - 4x^4$

3. Subtract: Subtract $2x^5 - 4x^4$ from the original polynomial: $(2x^5 - x^4) - (2x^5 - 4x^4) = 3x^4$

4. Repeat the process:

   • Divide $3x^4$ by $x$, which gives $3x^3$.
   • Multiply $3x^3$ by $x - 2$, getting $3x^4 - 6x^3$.
   • Subtract again, and continue this process until all terms are processed.

Would you like to continue with more details for this specific example?

Here are 5 related questions to consider:

1. How does polynomial long division differ from synthetic division?
2. Can polynomial division result in a remainder, and how is it handled?
3. What happens if the divisor is a binomial with more than a degree of 1 (e.g., $x^2 + bx + c$)?
4. What are the practical applications of polynomial long division?
5. How does the degree of the polynomial affect the number of steps in long division?

Tip:

Always ensure the terms of both the dividend and the divisor are in descending order of degree before starting polynomial long division.