Question

Factor the trinomial if possible. $$x^{2}+2 x+4$$

Short answer

The trinomial \(x^2 + 2x +4\) cannot be factored using real numbers.

Step-by-step solution

Identifying the Form

In the trinomial \(x^2 + 2x +4\), identification of the form \(x^2 + 2bx + b^2\) must be performed. For this specific case, b would have to be equal to \(2\), since \((2)^2 = 4\), which is the third term of the trinomial.

Checking for Trinomial Factorability

After identification, it is clear that the trinomial does not follow the form \(x^2 + 2bx + b^2\), since \(2x\) (the middle term of the trinomial) doesn't equal \(2*(2)*x\). Hence, this trinomial cannot be factored using real numbers.