We are given that $(x+2)$ is a factor of the quadratic $x^2 + Px - 10$. We need to find the value of $P$.

1. Problem Description

We are given that $(x+2)$ is a factor of the quadratic $x^2 + Px - 10$. We need to find the value of $P$.

2. Solution Steps

If $(x+2)$ is a factor of $x^2 + Px - 10$, then when $x=-2$, the quadratic expression must be equal to zero. This is due to the factor theorem.

So, we can substitute $x=-2$ into the equation $x^2 + Px - 10 = 0$.

$(-2)^2 + P(-2) - 10 = 0$

$4 - 2P - 10 = 0$

$-2P - 6 = 0$

$-2P = 6$

$P = \frac{6}{-2}$

$P = -3$

3. Final Answer

The value of $P$ is $-3$.

The correct option is B.