Question

What makes x^2-10x+ a perfect square trinomial?

Answer 1

For this case we have the following trinomial:
 $x^2 - 10x + a$
 We must complete squares to make it a perfect trinomial.
 Therefore, the value of a is given by:
 $a = (-10/2) ^ 2$
 Rewriting:
 $a = (-5) ^ 2 a = 25$
 Then, the polynomial is:
 $x ^ 2 - 10x + 25$
 Rewriting as a perfect square:
 $x ^ 2 - 10x + 25 = (x - 5) ^ 2$
 Answer:
 The value of a is:
 a = 25