Question

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

Answer 1

No, x^2 + 20x - 100 is not a perfect square trinomial.

Step-by-step explanation:

No, x^2 + 20x - 100 is not a perfect square trinomial.

In order for a trinomial to be a perfect square, it must be in the form (a + b)^2 or (a - b)^2.

The given trinomial can be factored as (x + 10)(x - 10), which is not in the form of a perfect square.

Answer 2

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.