https://file.aiquickdraw.com/mathbot/file/1726011862314fn7v7tvq.jpg

The equation visible in the image is:

\[
x^6 - x^5 - 3x^4 - 3x^3 + 2x^2 + 12x + 8 \div (x - 2)
\]

It appears to be asking for polynomial division, where we need to divide the polynomial \( x^6 - x^5 - 3x^4 - 3x^3 + 2x^2 + 12x + 8 \) by \( x - 2 \).

Let me perform this division using synthetic or long division.The result of dividing \( x^6 - x^5 - 3x^4 - 3x^3 + 2x^2 + 12x + 8 \) by \( x - 2 \) is:

\[
x^5 + x^4 - x^3 - 5x^2 - 8x - 4
\]

The remainder is 0, meaning the division is exact.

Would you like a detailed explanation of the division process or have any further questions? Here are some related questions to deepen your understanding:

1. How is polynomial long division performed step-by-step?
2. What does it mean when the remainder is zero in a division?
3. Can synthetic division be used for this type of problem?
4. How do we factor polynomials using division?
5. What are the applications of polynomial division in calculus?

**Tip**: Always check if the divisor is a factor of the polynomial by ensuring the remainder is zero after division!

x^6 - x^5 - 3x^4 - 3x^3 + 2x^2 + 12x + 8 ÷ (x - 2) = ?

Learn how to divide the polynomial x^6 - x^5 - 3x^4 - 3x^3 + 2x^2 + 12x + 8 by x - 2 using polynomial long division or synthetic division. This example covers key algebraic concepts in polynomial division, the factor theorem, and solving high-degree polynomials. Suitable for students in Grades 10-12.

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