What is the equation in factored form of the lowest degree p

What is the equation (in factored form) of the lowest degree polynomial with the zeroes -2, 1, and 5i where p(3)=7

Solution

The zeroes are -2,1,5i

And complex zeroes always occurs in pair so we have - 5i as a root too

And in factor form we can write it as

p(x)=(x+2)(x-1)(x+5i)(x-5i)

And p(3)=7

But here we get p(3)= 340

Therefore required polynomial is

p(x)= 7/340(x+2)(x-1)(x+5i)(x-5i)