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

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
${\Delta}_{x} = {b}^{2} - 4 a c$

So in this case you have
${\Delta}_{x} = {\left(- 28\right)}^{2} - 4 \cdot 16 \cdot 49 = 784 - 3136 < 0$
So you can't even factor this trinomial.

To sum up the concept:

• ${\Delta}_{x} < 0 \to$ not factorizable
• ${\Delta}_{x} = 0 \to$ perfect square (writable as ${\left(x - a\right)}^{2}$)
• ${\Delta}_{x} > 0 \to$ factorizable in the form $\left(x - a\right) \left(x - b\right)$