To factor the polynomial \(2x^3 + 5x^2 - x - 6\), we can use the method of factorization by grouping. Here are the steps:

1. **Group the terms**: 
\[2x^3 + 5x^2 - x - 6 = (2x^3 + 5x^2) + (-x - 6)\]

2. **Factor out the common terms in each group**:
\[= x^2(2x + 5) - 1(2x + 5)\]

3. **Factor out the common binomial factor**:
\[= (2x + 5)(x^2 - 1)\]

4. **Factor the difference of squares**:
\[= (2x + 5)(x + 1)(x - 1)\]

So, the factorization of \(2x^3 + 5x^2 - x - 6\) is:
\[ \boxed{(2x + 5)(x + 1)(x - 1)} \]

Would you like further details or have any questions?

Here are 5 questions you might be interested in asking next:
1. How do you factor a quadratic polynomial?
2. Can you explain the process of completing the square?
3. What is the quadratic formula and how is it derived?
4. How do you factor trinomials of the form \(ax^2 + bx + c\)?
5. What is synthetic division and how is it used in polynomial factorization?

**Tip:** When factoring polynomials, always look for a greatest common factor (GCF) first before proceeding to other methods such as grouping or using special formulas.

Learn how to factor the polynomial 2x^3 + 5x^2 - x - 6 using the grouping method and difference of squares with a detailed step-by-step solution. This problem covers polynomial factorization concepts and methods. Suitable for students in Grades 10-12.

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