# Question #ec668

Jul 31, 2017

$P = - 3$

#### Explanation:

Let ${y}^{2} - P y - 10$ be $f \left(y\right)$.

Since $y - 2$ is a factor of $f \left(y\right)$, equate $y - 2$ to zero and make $y$ the subject of the formula

$y - 2 = 0$

$y = 2$

Equate $f \left(y\right)$ to zero and substitute for $y = 2$

${y}^{2} - P y - 10 = 0$

${2}^{2} - 2 P - 10 = 0$

$4 - 10 - 2 P = 0$

$- 6 - 2 P = 0$

Make $P$ the subject of the formula

$- 6 - 2 P = 0$

$- 2 P = 6$

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

$P = - 3$