is this trinomial a trinomial square? x^2-12x+36

Question

anonymous · Answer

Can you factor it in the form (x-n)^2? If so, I'd say it is.
If you want to find n in this case, it would have to be the number is doubled to give -12 and multiplied by itself to give 36.

anonymous · Answer

the number which is*

keke1551 · Answer

i dont get it

anonymous · Answer

Yes it is!

anonymous · Answer

If the coefficient of the x^2 term is one, you can tell a perfect square trinomial if the last term is a positive perfect square, AND the ABSOLUTE value of middle term is equal to twice the root of the last term. Here is 36 a perfect square YES
Then is 12? = 2 x 6 YES

anonymous · Answer

The number, n, is 6. So the factored form of the trinomial is (x-6)^2.
You can test this by multiplying it out yourself, in this way...
(x-6)(x-6)
x multiplied by x gives x^2
x multiplied by -6 gives -6x
-6 multiplied by x gives -6x
-6 multiplied by -6 gives 36
Add all those terms together and you get
x^2 + -6x + -6x + 36
= x^2 -12x +36, which is the trinomial you started with. The method I described before, to find if it can be factored into a trinomial square, is a quick mental check. 

When you see a trinomial, you can think
1. What is half of the coefficient (the number next to the x) of the middle term?
2. What are the possible square roots of the last term? (if the term is negative, it doesn't have one, but if it's positive, it can have a negative and positive square root - for example, the square root of 36 could be -6 or 6)
3. Could the terms be the same number? If so, you have a trinomial square.

keke1551 · Answer

Thanks (:

anonymous · Answer

And as Shames rightly said, the coefficient of the x^2 term has to be 1 too, for it to be a trinomial square.

anonymous · Answer

:D

austinl · Answer

I realize the question is closed... but...The highest factor in the polynomial is to the second power. Therefore, it is a square. And there are three terms, therefore it is a trinomial!