Question

$\text{If} \: (x + 2) \: \text{and} \: (x - 1) \: \text{are factors} \\ \text{of} \: ( {x}^{3} + 10 {x}^{2} + mx + n) \: \text{then} \\ \text{find value for} \: m \: \text{and} \: n$

Answer 1

✌️✌️ hey mate,

P(x) = x³ + 10 x² + m x + n

x+2 is a factor: 

P(-2) = 0  =>  -8 + 40 - 2 m + n = 0


       =>  2m - n = 32  --(1)
x - 1 is a factor: 

P(1) = 0 =>    1 + 10 + m + n = 0


    = >     m + n = - 11  ---(2)

add the two:       

3m = 21  =>  m = 7


 n = -11 - 7 =  -18

thanks...
nice to help you ✌️✌️