Use the remainder theorum to find the value of 'k' for which (x+2) is a factor of (x+1)^7 + (2x+k)^3 .....   wats the value of k? ICSE 2013...sum from together with mathematics

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In remainder theorem if (x+a) is a factor of f(x) then f(-a) = 0

 

`f(x) = (x+1)^7+(2x+k)^3`

Since (x+2) is a factor `f(-2) = 0`

`f(-2) = 0`

`(-2+1)^7+(2xx-2+k)^3 = 0`

     `(k-4)^3 = 1`

     (k-4)^3 = (1)^3   

         `(k-4) = 1`

              `k = 5`

 

So the value of k is 5.

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