1. What is Factorization By Grouping?

Factorization by grouping is a method used to factor polynomials that have four or more terms. The terms are grouped in pairs and common factors are extracted from each pair.

2. How Does Factorization By Grouping Work?

The general approach for factorization by grouping:

Where:

• Group terms with common factors
• Factor out the greatest common factor from each group
• Factor out the common binomial factor

3. Steps For Factorization By Grouping

Step 1: Group terms that have common factors
Step 2: Factor out the GCF from each group
Step 3: Factor out the common binomial factor
Step 4: Verify by expanding the result

4. Using the Calculator

Tips: Enter polynomial terms separated by + signs. For example: 2x^2+4x+3x+6 or ax+ay+bx+by

5. Frequently Asked Questions (FAQ)

Q1: When should I use factorization by grouping?
A: Use this method when you have a polynomial with four or more terms that can be grouped into pairs with common factors.

Q2: What if the terms don't group nicely?
A: You may need to rearrange the terms or try a different factorization method such as quadratic formula or difference of squares.

Q3: Can all polynomials be factored by grouping?
A: No, only polynomials that have a specific structure where terms can be grouped and common factors extracted.

Q4: What's the difference between factoring and expanding?
A: Factoring breaks expressions into simpler multiplied factors, while expanding multiplies factors out into a sum of terms.

Q5: How do I check if my factorization is correct?
A: Multiply the factors back together - you should get the original polynomial expression.