Factoring with Higher Powers
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This lesson will review the process of factoring when there are higher powers involved.

 

Are there Common Factors?


If a common factor exists, its removal may lead to an expression which is a more recognizable form.

Examine: 

Factoring out the common factor of will reduce the expression, making it easily factorable.

  

 

 

Does the expression have even powers? 


Even powers in an expression may mean that the expression can be written as a "perfect square", and factored using the square root of the expression.

For example, may be written as
,

which factors into: 


 

  

Let's look at:

Re-writing into squares:

we factor into

The first parenthesis can be factored again to give us

 

Is there a variable in the power? 

If we multiply , we get .  This means

 that is a perfect square, or

So, to factor ,
we need to think of difference of perfect squares.

Try the example to the right.
 

  

Factor:

Factors of  -32 that yield the
sum of +4 are ( 8 )( - 4).

For the first term, remember that = .

The expression would
factor into