Question

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

Answer 1

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)`