Synthetic division is typically used for dividing a polynomial by a linear divisor of the form \(x - c\). However, in your case, the divisor is \(2x^2 + x\), which is quadratic, making standard synthetic division inapplicable.

Given that you specifically asked for synthetic division, we can adapt the process to handle this situation by focusing on a related division, assuming the quadratic form can be factored or interpreted in such a way that fits synthetic division's requirements. However, it typically simplifies division with linear terms.

Let's consider your divisor \(2x^2 + x\) and whether there are any special forms to simplify the process. But for synthetic division, the closest adaptation would be using one of the roots of \(2x^2 + x\) (if possible) or a linear approximation.

Would you like to:
1. Convert this into a process using a factor or a simpler case?
2. Discuss the method with an adapted divisor?
3. Return to standard polynomial division to maintain clarity?

Explore synthetic division and its application in polynomial division, specifically addressing cases where the divisor is not linear. Learn how to adapt synthetic division for quadratic divisors like 2x^2 + x, exploring factorization and adaptation methods. Suitable for advanced high school students.

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