Is the following trinomial a perfect square?

Say you had x^2+6x+8= y and for whatever algebraic reasons, needed it to be a pefect square. Well, think about FOIL. The two binomials that get you the closet answer are (x+3)(x+3), which is x^2+6x+9. So, to complete the square, you would add 1 to both sides, producing (x+3)^2.

The important thing there is to know the relationship between (x+3) and (x^2+6x+9). The easiest thing to notice is that all of the integers are multiples of three: 6= 3 x 2, and 9= 3 x 3.

Or, 6 is 2 x 3 and 9 is 3^2.

So, the rule is, when you have a polynomial x^2 + ax + b, if b = (1/2 a)^2, then the trinomial is a perfect square. Or in laymen’s terms, if one half of a is the square route of b, then it’s square.

So now you tell us: is it?