Question is in the photo.

Step-by-step explanation:

We are finding a polynomial of degree 3.

Since 4 and 5i are the zeroes of the polynomial,

the conjugate -5i must also be such a zero.

=> f(x) = a(x - 4)(x - 5i)(x + 5i)

=> f(x) = a(x - 4)(x² - 25i²)

=> f(x) = a(x - 4)(x² + 25)

When x = 1, f(1) = -234.

=> a(1 - 4)(1² + 25) = -234

=> a(-3)(-26) = -234

=> -78a = -234

=> a = 3

Hence,

f(x) = 3(x - 4)(x² + 25) = 3x³ - 12x² + 75x - 300.

42

step-by-step explanation: