could someone help me with my math homework?

Question

i need help learning how to create a polynomial function from given zeros. and i currently have no clue on how to do it!

ex.1 Write the polynomial function given that -3 and 5 + √2 are zeros.

ex.2 Write the polynomial function given that -5 and 2i are zeros.

Answer 1

1) if n is a zero, then x - n is a factor learn that!

2) complex zeros come in conjugate pairs learn that!

f(x) = (x + 3)(x - (5 + √2)

f(x) = (x + 5)(x - 2i)(x + 2i)