precal question

Question

Find all zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

P(x) = x⁴ − 3x³ − 3x² − 3x − 4

x=

Answer 1

There can only be one positive root, and with the only positive coefficient with the largest power, we are guaranteed there will be one.

4 | 1 -3 -3 -3 -4

4 4 4 4

1 1 1 1 0

x^3 + x^2 + x + 1 = (x + 1)(x^2 + 1)

Thus, the original polynomial factors as (x-4)(x + 1)(x^2 + 1) or (x-4)(x + 1)(x + i)(x - i)

Thus, we have real roots -1 and 4; if we are including complex roots, also, roots are -1,-i, i, 4