Use the factor theorem to find the value of `k` for which `(a+2b),w h e r ea ,b!=0` is a factor of `a^4+32 b^4+a ^3b(k+3)dot`

Explanation

Let `f(a) = a^(4) + 32b^(4)+ a^(3) b (k+3)` . If (a+2b) is factor of f(a), then
`f(-2b) = (-2b)^(4)+ 32b^(4) + (-2b)^(3) b (k+ 3) = 0 `
or ` 48 b^(4) - 8b^(4)(k+3) = 0`
or `8b^(4) [ 6-(K+3)]=0`
or `8b ^(4) (3-k) = 0`
Since b `ne` 0, so 3 - k = 0 or k = 3