(Easy 10 points) Write a polynomial function with following characteristics

That it has these following characteristics. (There are no other characteristics, these are the exact ones provided.)

Real number coefficients.
Zeros at 2, -5, 2+i
f(0) = -150

Please show any work so I can understand. 10 points to best answer! Thanks!

The complex number 2 + i is a root, so its conjugate, 2 - i, must also be a root. That gives us four known roots. There may be others, and some of these roots may be repeated.

f(x) = p(x)(x - 2)(x + 5)[x - (2 + i)][x - (2 - i)], where p(x) is a polynomial
f(x) = p(x)(x - 2)(x + 5)(x² - 4x + 5)

f(0) = -150
p(0)(-2)(5)(5) = -150
-50p(0) = -150
p(0) = 3

There are any number of polynomials fitting the bill. Here are a few that work:

f(x) = 3(x - 2)(x + 5)(x² - 4x + 5)
f(x) = (x + 3)(x - 2)(x + 5)(x² - 4x + 5)
f(x) = (x² + 3)(x - 2)(x + 5)(x² - 4x + 5)