Question

If (x+2) and (x-1) are factors of x³+10x²+mn+n then What is the value of m and n.

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Answer 1

$\huge\mathcal\blue{answer}$

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

Answer 2

Answer:

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

Step-by-step explanation:

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