# Help!! I need help figuring out this polynomial function!!!?

• Help!! I need help figuring out this polynomial function!!!?  Answer #1 | 05/01 2014 11:38 First, factor out x x(2x^4 - 7x^3 - 10x^2 + 33x + 18) so one rational zero is x = 0. If there is another rational zero, besides x = 0, the top would have to be a factor of the constant term, 18, and the bottom would have to be a factor of the leading coefficient, 2 so possible are (each is ±) 18/1, 18/2, 9/1, 9/2, 6/1, 6/2, 3/1, 3/1, 1/1, 1/2 so you hope to guess one soon. 1 visually does not work; I;ll start by trying -1. With synthetic division, you'd need the remainder to be 0 for -1 to be a zero (and x + 1 to be a factor) so... -1 | 2 -7 -10 33 18 ..... 2 -9 -1  34 -16 no good so try -2 -2 | 2 -7 -10 33 18 .... 2 -11 12 9 0 it worked so (x + 2) is a factor. Try it again with the new dividend -2 | 2 -11 12 9 ..... 2 -15 42 . nope so try 3 3 | 2 -11 12 9 .... 2 -5   -3 0 worked so (x - 3) is a factor... and now you have a quadratic, 2x^2 - 5x - 3 which you can do by reverse FOIL: (2x + 1)(x - 3) so the other two zeros are -1/2 and 3 (making 3 a zero of multiple 2 since it happened twice) and you can use this to answer the questions. 