Question

What is the correct description for the polynomial? (x²+4)

difference of two squares,
general trinomial,
perfect square trinomial,
prime,

Answer 1

difference of two squares

Explanation:

As you can see there are two terms, `x^2` and `4`. That makes it a binomial, not a trinomial so we can rule out two of the options leaving us with prime and the difference of two squares.

A prime polynomial is one that cannot be factorized. This polynomial can be factorized to `(x+2i)(x-2i)` meaning it is not prime.

The difference of two squares can be expressed as follows: `a^2-b^2 = (a+b)(a-b)`

As we can see this binomial can be expressed in this form
`x^2-4= x^2-(2i)^2 = (x+2i)(x-2i)`