Factoring by Grouping

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

1) 2x^2 + x - 15

2) 4x^2 - 12x - 7

3) 2x^2 - 21x + 49

4) 2x^2 + 9x - 81

5) 2x^2 - 9x - 18

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