Question 77225: Please help.
Determine whether the following trinomial is a perfect square. If it is, factor the trinomial.
x^2 - 24x +48 Found 2 solutions by THANApHD, jim_thompson5910:Answer by THANApHD(104) (Show Source):
You can put this solution on YOUR website! If it is a perfect square, then
[(middle term)/2x]^2 = last term
(24x/2x)^2 = 144
which is not equal to last term so it is not a perfect square
You can put this solution on YOUR website! If we have something like this:
If we look at the last term, we can determine if the trinomial is a perfect square. If the last term is a perfect square, then we take the square root and then double that value to get the middle term. If the middle term equals and c is a perfect square, then we have a trinomial that is a perfect square. Since 48 is not a perfect square, the entire trinomial is not a perfect square. It's that simple. This idea can be applied to something like this:
Since 9 is a perfect square, we take the square root of 9 to get 3, and then double 3 to get 6. This shows that the trinomial is a perfect square.
(