1
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what number can you add to x squared minus 6x to complete the perfect square trinomial so trinomial is

2
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just a polynonial with 3 terms so right now we have 2 terms so they are essentialy saying can we add

3
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a term here essentially a number constant so this comes a perfect square the expression once becomes

4
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a trinomial becomes a perfect square so let me just write it here x squared minus 6x so we are going

5
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to add something right here so that the expression can be a perfect square a perfect square of a binomial

6
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and to think about that lets think about what a perfect square would look like so let's immagine if

7
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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

8
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constant a squared well this is the same thing as x plus a times x plus a and this is the same thing

9
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as you might remember this pattern well just multiply it out well just multiply x by everything here

10
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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

11
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a squared that all just comes out of doing the distubutiver property twice or you could think of it as

12
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foil if you find that a little bit easier and this gives you x squared plus 2ax plus a squared so if

13
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you have a trinomial in this form it is a perfect square and it can be factored out into x plus a squared

14
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and we see the pattern here in both cases its a coefficient on the x squared term is 1 and then we see

15
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whatever the coefficient here is on the first degree term on the x what ever half that number is and

16
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we square it and make that the constant then this will be a perfect square for example 1/2 of 2a is a

17
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and we are squaring a right over here and that makes it a perfect square so let's do the same thing with

18
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our binomial soon to be a trinomial lets look at the first degree coefficient it is a -6 you can view

19
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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

20
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just pattern match right over here so what would a be? a would equal to -3 and so if we added a squared

21
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to this expression it would be a perfect square so we literally just took half of this which is -3

22
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and then we are going to square it so -3 squared is positive 9 so this over here is just a squared notice

23
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I called this 2a and took half of it to figure out what a is and I squared it to get this nine here so

24
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I just took -6 divided by 2 is -3 squared it and got 9 and if you wanted to factor this out we have x

25
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squared minus 6x plus 9 so what 2 numbers when you take their product you get 9 and when you add them

26
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together you get -6 well -3 and -3 so this is going to be x-3 times x-3 or you could think of it as

27
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x-3 squared so it is a perfect square trinomial