Question

Main Idea: Using the grouping method to factor a polynomial is like using the distributive property in reverse.
Polynomials and the Distributive Property
Words
Using the distributive property multiplies factors together to form a product.
Using the distributive property in reverse divides a
i Answer,
out of
====
a product.
Variables
a(b + c) = ab + ac
ab + ac =
i Answer

Polynomials 6xx+2) = 6x7+12x
6x2+12x=
Answer
-==-
a(b+ c)
factor
6x(x +2)

Answer 1

It looks like you're discussing the relationship between the distributive property and factoring polynomials using the grouping method. Let's fill in the missing parts and clarify the concepts you're exploring.

### Main Idea:
Using the grouping method to factor a polynomial is like using the distributive property in reverse.

### Polynomials and the Distributive Property

**Words:**
Using the distributive property multiplies factors together to form a product.
Using the distributive property in reverse divides a factor out of a product.

**Variables:**
The distributive property is expressed as:
**a(b + c) = ab + ac**
In reverse, if you have:
**ab + ac = a(b + c)**
you can factor out the common factor 'a'.

### Example with Polynomials:
Consider the polynomial **6x² + 12x**.

You can factor it as follows:
1. Identify the common factor in each term. Here, both terms have a common factor of **6x**.
2. Factor out the common factor:
**6x² + 12x = 6x(x + 2)**

So, the answer to the factoring process is:
**6x(x + 2)**

### Summary of the Process:
- **Identify common factors** in the polynomial.
- **Factor** out the common factors using the distributive property in reverse.

Using this method helps to simplify polynomials and makes solving equations easier.