https://file.aiquickdraw.com/mathbot/file/17300926263234w2updc5.jpg

To factor the given quadratic expression completely, \(6x^2 - 3x - 9\), follow these steps:

1. **Factor out the greatest common factor (GCF):**
   The GCF of \(6x^2\), \(-3x\), and \(-9\) is 3. Factoring out 3 gives:
   \[
   6x^2 - 3x - 9 = 3(2x^2 - x - 3)
   \]

2. **Factor the quadratic expression \(2x^2 - x - 3\):**
   We need two numbers that multiply to \(2 \times -3 = -6\) and add to \(-1\). These numbers are \(-3\) and 2.

3. **Rewrite the middle term using \(-3\) and 2:**
   \[
   2x^2 - 3x + 2x - 3
   \]

4. **Factor by grouping:**
   Group the terms:
   \[
   (2x^2 - 3x) + (2x - 3)
   \]
   Factor out the common factors from each group:
   \[
   x(2x - 3) + 1(2x - 3)
   \]
   Now factor out the common factor \((2x - 3)\):
   \[
   (2x - 3)(x + 1)
   \]

5. **Combine the factored forms:**
   The completely factored form is:
   \[
   3(2x - 3)(x + 1)
   \]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would you factor \(4x^2 - 9x + 5\)?
2. What is the process for factoring trinomials where the leading coefficient is not 1?
3. How do you check if a quadratic expression can be factored completely?
4. What happens if a quadratic has no real factors? How would you solve it then?
5. Can you factor \(3x^2 - 12x + 12\) completely?

**Tip:** When factoring quadratics, always start by factoring out the greatest common factor before dealing with the trinomial itself.

Step-by-step guide on how to factor the quadratic expression 6x^2 - 3x - 9 completely. Learn the factoring process, including factoring out the greatest common factor and using grouping. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation