Question 330746
<br>{{{49a^2+4-28a}}} <br>

{{{49a^2-28a+4}}}<br>

We must use the factors of the first term to see how this can be factored, using either 49 and 1, or 7 and 7.<br>

{{{(49a-somenumber)(a-somenumber)}}} or {{{(7a-somenumber)(7a-somenumber)}}}<br>

Notice that both factors must have a negative sign in them, since the last term is positive, but the middle term is negative.<br>

Then we just have to use the factors of 4 to see what numbers will work to factor this. <br> 

This is just a matter of guessing and checking, or trial and error.  Factors of 4 are 4 and 1, or 2 and 2.  So our answer MUST be one of the following, if this polynomial is factorable:<br>

{{{(49a-4)(a-1)}}} or {{{(49a-1)(a-4)}}} or {{{(49a-2)(49a-2)}}} or<br>

{{{(7a-4)(7a-1)}}} or {{{(7a-2)(7a-2)}}}<br>

Upon closer inspection, we can see that:<br>

{{{(7a-2)(7a-2)}}} does indeed multiply out to {{{49a^2-28a+4}}}<br>

so the answer is {{{(7a-2)(7a-2)}}}<br>

This polynomial is a special one, in the form of:<br>

{{{a^2-2ab+b^2=(a-b)^2}}}<br> 

where {{{a=7a}}} and {{{b=2}}}<br>

Factoring polynomials is hard, and it takes a lot of practice.  There are also different ways to approach this problem, but I hope this helps!