f(x)=x^4 - x^3 + 7x^2 -9x-18

Question

use synthetic division to find actual roots from the list above. start with the roots that are closest to the origin. that each new trial divisor using the previous resulting depressed polynomial

Answer 1

-1 l 1 -1 7 -9 -18

-1___2___-9____18

1 -2 9 -18 0

f(x) = (x+1)(x³ - 2x² + 9x - 18)

2 l 1 -2 9 -18

______2___0____18

1 0 9 0

f(x) = (x+1)(x-2)(x²+9)

f(x) = (x+1)(x-2)(x-3i)(x+3i)

The roots are -1, 2, 3i, and -3i.