The given expression is a special binomial, known as the "difference of squares". A difference of squares binomial has the given factorization: . Thus, we can rewrite  as  and it follows that 

The product of is .

For the equation , 

must equal and  must equal .

Thus  and must be and , making the answer  .

The quadratic can be solved as . Setting each factor to zero yields the answers.

Because both terms are perfect squares, this is a difference of squares:

The difference of squares formula is .

Here, a = x and b = 5.  Therefore the answer is .

You can double check the answer using the FOIL method:

The solutions indicate that the answer is:

and we need to insert the correct addition or subtraction signs. Because the last term in the problem is positive (+4), both signs have to be plus signs or both signs have to be minus signs. Because the second term (-5x) is negative, we can conclude that both have to be minus signs leaving us with:

Because the term doesn’t have a coefficient, you want to begin by looking at the  term () of the polynomial: .  Find the factors of  that when added together equal the second coefficient (the term) of the polynomial. 

There are only four factors of : , and only two of those factors, , can be manipulated to equal  when added together and manipulated to equal  when multiplied together: (i.e.,). 

Because the  term doesn’t have a coefficient, you want to begin by looking at the  term () of the polynomial: . 

Find the factors of  that when added together equal the second coefficient (the  term) of the polynomial: . 

There are seven factors of : , and only two of those factors, , can be manipulated to equal  when added together and manipulated to equal  when multiplied together:  

The given expression can be re-written as:

Cancel (2x - 5):

Factor out the 7:

Take the 8 from the x-term, cut it in half to get 4, then square it to get 16.  Make this 16 equal to C/7:

Solve for C:

We can factor this trinomial using the FOIL method backwards. This method allows us to immediately infer that our answer will be two binomials, one of which begins with  and the other of which begins with . This is the only way the binomials will multiply to give us .

The next part, however, is slightly more difficult. The last part of the trinomial is , which could only happen through the multiplication of 1 and 2; since the 2 is negative, the binomials must also have opposite signs.

Finally, we look at the trinomial's middle term. For the final product to be , the 1 must be multiplied with the  and be negative, and the 2 must be multiplied with the  and be positive. This would give us , or the  that we are looking for.

In other words, our answer must be 

to properly multiply out to the trinomial given in this question.