Find the zeroes of the polynomial using any combination of the rational roots theorem, synthetic division, testing for 1 and -1, and/or the remainder and factor theorems. p(x) = x⁴ + 3x³ + 3x² - 17x - 18 A) -1, 2, B) 1, -2, C) -1, 2, D) 1, -2,

Question

Quizplus · Accepted Answer

We can use synthetic division to test the rational roots and get:

-1 | 1 111 1114 2 2 -17 -18
    -1 -10 6 -8 6 11 
   ------------------
    1 110 1104 2 -15 -7

2 | 1 111 1114 2 2 -17 -18
   2 26 1160 244 492 950
  --------------------
   1 113 2754 246 494 932

No rational roots have been found. We can try testing for 1 and -1, but this does not give us any roots either. Therefore, we can conclude that the zeroes are irrational or complex.

Find the Zeroes of the Polynomial Using Any Combination of the Rational