what number can you add to x squared minus 6x to complete the perfect square trinomial so trinomial is just a polynonial with 3 terms so right now we have 2 terms so they are essentialy saying can we add a term here essentially a number constant so this comes a perfect square the expression once becomes a trinomial becomes a perfect square so let me just write it here x squared minus 6x so we are going to add something right here so that the expression can be a perfect square a perfect square of a binomial and to think about that lets think about what a perfect square would look like so let's immagine if we had x plus a squared what would that look like if we were to expand it out let me do this in another color to show you it is a side note so I'll do it in blue so if I had x plus some constant a squared well this is the same thing as x plus a times x plus a and this is the same thing as you might remember this pattern well just multiply it out well just multiply x by everything here so x timesx is x squared then x times a is a x then a times x is a x then we have a times a which is a squared that all just comes out of doing the distubutiver property twice or you could think of it as foil if you find that a little bit easier and this gives you x squared plus 2ax plus a squared so if you have a trinomial in this form it is a perfect square and it can be factored out into x plus a squared and we see the pattern here in both cases its a coefficient on the x squared term is 1 and then we see whatever the coefficient here is on the first degree term on the x what ever half that number is and we square it and make that the constant then this will be a perfect square for example 1/2 of 2a is a and we are squaring a right over here and that makes it a perfect square so let's do the same thing with our binomial soon to be a trinomial lets look at the first degree coefficient it is a -6 you can view this right over here as our 2a and so what is half of this or in others words 2a is equal to -6 if we just pattern match right over here so what would a be? a would equal to -3 and so if we added a squared to this expression it would be a perfect square so we literally just took half of this which is -3 and then we are going to square it so -3 squared is positive 9 so this over here is just a squared notice