### Concept (1)

The first step is to identify the polynomial type in order to decide which factoring methods to use. Next, look for a common term that can be taken out of the expression. A statement with two terms can be factored by a difference of perfect squares or factoring the sum or difference of cubes. For the case with four terms, factoring by grouping is the most effective way. This method is explained in the video on advanced factoring.

### Sample Problems (13)

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Factor:

2x²(x + 1)² − 7x(x + 1)² + 6(x + 1)²
###### Problem 1
How to factor by taking out the greatest common factor.

Factor:

2ab² − 8b² − a + 4
###### Problem 2
How to factor by grouping.

Factor:

16x² − 24xy + 9y²
###### Problem 3
How to factor a perfect square trinomial.

Factor:

8x³ − 27
###### Problem 4
How to factor the difference of cubes.

Factor:

10x² + 23xy − 5y²
###### Problem 5
How to factor a trinomial with a leading coefficient not equal to one.
###### Problem 6
Factoring using a "u" substitution to reduce the degree of the polynomial.
###### Problem 7
Review of the possible methods of factoring presented in a flow map based on the polynomial degree.
###### Problem 8
Factoring that results in perfect square binomials and verifying the solution using FOIL.
###### Problem 9
Factoring four term polynomials using factoring by grouping.
###### Problem 10
How to factor trinomials using guess and check and verify using FOIL.
###### Problem 11
Review of the methods for factoring a binomial, including greatest common factor, difference of perfect squares, and sum or difference of cubes formulas
###### Problem 12
How to factor a trinomial by re-writing it with four terms and using factoring by grouping.
###### Problem 13
Geometric area, or diamond and box method for factoring trinomials.