How to solve all polynomials problems in college algebra.

A great way to solve polynomials is using the factorization. This method will be explained in general followed by an example. The rules are as follows: 

Step 1: 

The equation needs to be written in the correct form. This means that all parentheses on both sides of the equation should be evaluated by distributing, adding and subtracting all terms and then set the equation equal to zero with the terms written in descending order ( eg. x^3 + 2*x^2 + x = 0, and not: x+ 2*x^2 + x^3 = 0) 

Step 2: 

Use any correct factorization method to solve the problem (eg. common factor, foil method,etc.) 

Step 3: 

Use the Zero Product Property and set each factor containing a variable equal to zero.

Step 4: 

Solve each factor that was set equal to zero by getting the variable (x, y, z, etc. - depending which variable is being used) on one side and the answer on the other side. 

LET's DEMONSTRATE THIS WITH AN EXAMPLE: 

`4x^2 = 12x`

Step 1: Write in the correct form 

`4x^2 - 12x = 0`

Step 2: Use correct factorization method: In this example we take out '4x' as a common factor:

`4x(x - 3) = 0`

Step 3: Zero Product Property

`4x = 0 or x-3=0`

Step 4 : Solve each factor and obtain variable on one side and the answer on the other side: 

First evaluate the first factor:

`4x = 0`

`x = 0`

OR

The second factor: 

`x-3=0`

`x = 3`

ANSWER: `x=0 or x=3`

Hope this helps!