How can you tell if a polynomial is a perfect square?

Answer 1

Let's take a quadratic polynomial. There are three terms in a quadratic polynomial. Example:

X^2 + 8X + 16 = 0

To satisfy the criteria of a perfect square polynomial, the first and last term of the polynomial must be squares. The middle term must be either plus or minus two multiplied by the square root of the first term multiplied by the square root of the last term. If these three criteria are satisifed, the polynomial is a perfect square. Let us take the above quadratic.

X^2 + 8X + 16 = X^2 + 2(4X) + 4^2 = (X+4)^2

As we can see, each criteria is satified and the polynomial does indeed form a perfect square.