How do you know if 49x^2 − 28x + 16 is a perfect square trinomial and how do you factor it?

1 Answer
Jun 8, 2015

I usually try to calculate the Delta_x. If it is equal to zero it is a perfect square.
You can calculate it using the formula
Delta_x=b^2-4ac

So in this case you have
Delta_x=(-28)^2-4*16*49=784-3136<0
So you can't even factor this trinomial.

To sum up the concept:

  • Delta_x<0 -> not factorizable
  • Delta_x=0 -> perfect square (writable as (x-a)^2)
  • Delta_x>0 -> factorizable in the form (x-a)(x-b)