how do we do this

Question

12a^3-9a^2+4a-3

Answer 1

Factor by regrouping,

 

12a^3-9a^2+4a-3

= 3a^2(4a-3) + (4a-3)

= (3a^2+1)(4a-3)

Answer 2

Is it:   12a³ - 9a² + 4a - 3  ??

 

If so,  you can notice that the first two terms do have a common factor.  I can divide both by 3 and also by a².  This is called factoring.

 

Let's try that:   3a²(4a - 3) + 4a - 3,  ok?  It has three terms now.

 

Now look at it.  Do you see that 4a - 3 appears twice!  Cool.  

 

Let's rewrite it with parenthesis:   3a²(4a - 3) + (4a - 3).   Aha!  Now we have only 2 terms and we can factor out the (4a - 3) by dividing both terms.

 

but first i'll rewrite it again for clarity:  3a²(4a - 3) + 1(4a - 3)     [note that 1(4a - 3) is the same as (4a - 3)]

 

so we factor out the (4a - 3) from both terms to get (4a - 3)*(3a² + 1)

 

so i believe your answer is (4a - 3)*(3a² + 1) or (3a² + 1)*(4a - 3) which is the same.