Question

Is x^2 + 20x - 100 a perfect square trinomial? Explain why or why not.

Answer 1

No.

This is almost a perfect square trinomial, but it is not.

We can verify this by looking at the first two terms.

With only x^2 + 20x, we could complete the square to make this a perfect square trinomial by performing the following steps:

Divide the middle term by 2.

20 / 2 = 10

Square the quotient.

10^2 = 100.

Add 100 to both sides.

x^2 + 20x + 100 = 100

As the provided trinomial is x^2 + 20x - 100, it is not a perfect square trinomial.