1. **State the problem:** We are given the polynomial function $P(x) = x^2 + x + 2$ and asked to find the value of $P(0)$. 2. **Recall the formula:** To find $P(0)$, substitute $x = 0$ into the polynomial expression. 3. **Substitute and simplify:** $$P(0) = 0^2 + 0 + 2$$ $$P(0) = 0 + 0 + 2$$ $$P(0) = 2$$ 4. **Conclusion:** The value of $P(0)$ is 2. This means when $x$ is zero, the polynomial $P(x)$ evaluates to 2.