Question

.

Answer 1

?

Answer 2

use the given hint

Answer 3

whats the conjugate pair of 3-i ?

Answer 4

conjugate of 3-i is 3+i

Answer 5

the hint says the imaginary roots come in conjugate pairs so
both 3-i and 3+i will be roots

Answer 6

that means you need to find a polynomial with roots :
\[4, ~3-i, ~3+i\]

Answer 7

use factor theorem :
if "k" is a root of polynomial, then (x-k) is a factor

Answer 8

so a polynomial with those roots can be represented as :
\[(x-4)(x-(3-i))(x-(3+i))\]

Answer 9

simplify