could someone help me with trinomials?

Question

Factor the following problem completely. First factor out the greatest common factor, and then factor the remaining trinomial.

 

100a⁴-900a³ +1800a²

Answer 1

Note that the coefficients of each term is a multiple of 100.  Also, each term has an a² in common because if you break them up into factors, there is a factor such that a² for each term in the expression.  Therefore, the greatest common factor is 100a².

 

So factoring using the greatest common factor yields

 

100a²(a² - 9a + 18)

 

 

But we are not done yet.  The factor in parenthesis can be factored using FOIL.  As a result, our final factored form is

 

100a²(a - 6)(a - 3)