Is this trinomial a perfect square
x^2-6x+9
if the trinomial starts with x^2 and 1/2 of the middle term coefficient squared equals the last term, then it is a perfect square.
tell me what you found.
i thought it was not a perfect square. because i tried factoring it but it won't come out.am i wrong then
expand (x+3)^2
(x+3)(x+3)
x^2+3x+3x+9
x^2+6x+9
but in the original is x^2-6x+9
(x+3)^2 is incorrect. It is (x-3)^2:
x^2-3x-3x+9
x2-6x+9
and there is your answer.
Do you get it?
(x-3)(x-3)
x^2-3x-3x+9
x^2-6x+9
therefore it is a perfect square is this correct then
sorry emily, of course I meant (x-3)^2, it was a typo. sorry, its getting late where I am.
Yes it is. Good job!
Yes, you are correct. The trinomial x^2-6x+9 is a perfect square. To determine this, you can use the fact that if the trinomial starts with x^2 and the middle term coefficient squared equals the last term, then it is a perfect square.
In this case, x^2 is the first term, and the middle term coefficient is -6, so we check if (-6/2)^2 = 9.
(-6/2)^2 = (-3)^2 = 9
Since the last term is equal to (-6/2)^2, which is 9, the trinomial x^2-6x+9 is indeed a perfect square.
To verify this, you can also expand (x-3)^2:
(x-3)(x-3) = x^2 - 3x - 3x + 9 = x^2 - 6x + 9
So, x^2-6x+9 is equal to (x-3)^2, confirming that it is a perfect square.
Great job!