# If (x-2).P(x)= 3x^3+ax-10 , what is P(-1) ?

##### 1 Answer

From $\left(x - 2\right) P \left(x\right) = 3 {x}^{3} + a x - 10$ for $x = 2$ we get

$\left(2 - 2\right) P \left(2\right) = 3 \cdot {2}^{3} + 2 a - 10 \implies 0 = 14 + 2 a \implies a = - 7$

Hence the relation becomes

$\left(x - 2\right) P \left(x\right) = 3 {x}^{3} - 7 x + 10$

For $x = - 1$ then

$\left(- 1 - 2\right) P \left(- 1\right) = - 3 + 7 + 10 \implies P \left(- 1\right) = - \frac{14}{3}$