The process of factoring a polynomial may have several steps before reaching the final answer. In this presentation, we will factor expressions with greatest common factors, special products, quadratic trinomials, or polynomials by grouping.

2. 10.8 FACTORING USING THE DISTRIBUTIVE PROPERTY.
When we want to factor a polynomial, the first thing that must be observed is the
number of terms the expression has.
We do this in order to choose the correct factoring method for the given
polynomial.
A suggested guideline to factor completely a polynomial is the following:
Identify the
Greatest
Common
factor
Identify Special
Products
Identify
quadratic
trinomials
More than 4
terms:
grouping

3. 10.8 FACTORING USING THE DISTRIBUTIVE PROPERTY.
The first element that must be identified is the greatest common factor of the
polynomial expression. To do this, we need to identify the repeated element in
the coefficients and in the variables of the expression.
Example: factor the GCF out of the given polynomials.
𝟏. 𝟑𝟑𝒙 𝟓
− 𝟏𝟐𝟏𝒙 𝟐
𝟐. 𝟏𝟐𝒙 𝟐
+ 𝟐𝟕𝒙
𝟑. −𝟔𝒙 𝟑 − 𝟏𝟓 𝟒. 𝟖𝒙 𝟓 + 𝟒𝒙 𝟐 − 𝟐𝒙

4. 10.8 FACTORING USING THE DISTRIBUTIVE PROPERTY
Once the GCF has been identified, we proceed to check for special products or any
of the possible factoring methods for quadratic trinomials.
Example: factor completely the following polynomials.
𝟏. 𝟒𝒙 𝟐 + 𝟑𝟔 𝟐. 𝟒𝒙 𝟐 − 𝟑𝟔
𝟑. 𝟏𝟐𝒙 𝟐 − 𝟏𝟐𝒙 + 𝟑 𝟒. 𝟏𝟎𝟎𝒙 𝟑 + 𝟐𝟖𝟎𝒙 𝟐 + 𝟏𝟗𝟔𝒙

5. 10.8 FACTORING USING THE DISTRIBUTIVE PROPERTY.
𝟓. 𝟓𝒙 𝟑
− 𝟐𝟓𝒙 𝟐
− 𝟑𝟎𝒙 𝟔. 𝟕𝟓𝒙 𝟒
− 𝟑𝒙 𝟐
𝟕. 𝟐𝒙 𝟑
− 𝟔𝒙 𝟐
+ 𝟒𝒙 𝟖. 𝟏𝟐𝒙 𝟑
− 𝟏𝟒𝒙 𝟐
− 𝟔𝒙

6. HOMEWORK:
PG. 629
EXERCISES 6 TO 8, 15 TO 28

7. 10.8 FACTORING USING THE DISTRIBUTIVE PROPERTY
FACTOR BY GROUPING.
This process is applied when the polynomial expression contains 4 or more
terms. The main objective is to group elements that have common factors, in
order to factor them. Finally, we analyze what is left, looking for special products,
trinomials, etc…

8. 10.8 FACTORING USING THE DISTRIBUTIVE PROPERTY
Examples: factor completely the given polynomials.
𝟏. 𝒙 𝟑 + 𝟒𝒙 𝟐 + 𝟔𝒙 + 𝟐𝟒
𝒙 𝟑 + 𝟒𝒙 𝟐 + 𝟔𝒙 + 𝟐𝟒 Group terms with common factors
𝒙 𝟐
𝒙 + 𝟒 + 𝟔 𝒙 + 𝟒 Factor the GCF from the small parenthesis
𝒙 + 𝟒 𝒙 𝟐
+ 𝟔 Identify more common factors, and simplify
As you can see, the main objective is to find GCF and use the Distributive
Property to group elements in a polynomial.

9. 10.8 FACTORING USING THE DISTRIBUTIVE PROPERTY
𝟐. 𝒙 𝟑 + 𝟐𝒙 𝟐 − 𝟑𝟔𝒙 − 𝟕𝟐 𝟑. 𝟐𝒙 𝟑 + 𝟑𝒙 𝟐 − 𝟓𝟎𝒙 − 𝟕𝟓