Introduction
Many students are discouraged when they see large problems to factor. Factoring by grouping is a method of factoring that works on four-term polynomials that have a specific pattern to them.
Task
You will be able to factor many equations by grouping by the end of this webquest.
Process
Factor: x3 + 3x2 + 2x + 6
1. Rearrange the terms so that the exponents are in decreasing order, if they aren't already.
2. Group the first two and the last two terms together. (x3 + 3x2) + (2x + 6)
3. Factor each of the two groups separately. In our example, you can factor an x2 out of the first group and a 2 out of the second. x2(x + 3) + 2(x + 3)
4. Factor the common factor out of the two groups. In our example, both of the groups have an x + 3 in common. That's what we'll factor out. (x + 3)(x2 + 2)
5. Check the two factors to see if they can be factored further. Neither x2 + 2 or x + 3 can be factored further so (x + 3)(x2 + 2) is our final answer. (x + 3)(x2 + 2)
Evaluation
Try to apply what you have learned so far to complete these equations
Conclusion
Hopefully the lesson has helped you complete equations with answers as seen below.
1) (x+3)(2x-5)
2) (2x+1)(2x-7)
3) (x-7)(2x-7)
4) (x+9)(2x-9)
5) (2x+3)(x-6)
Credits
Teacher Page
Amarion and Xavier
Killeen Career Center