rational zeros f(x)=x^3+10x^2+14x-6

Question

f(x)=x^3+10x^2+14x-6 Use the Rational Zero Therom to list all the possible rational zeros.

Answer 1

The rational zeroes are factors of the constant 6. The list consists of all these factors in their positive and negative forms: 1, -1, 2, -2, 3, -3, 6, -6. The actual (integer) zeroes, if any, are found by plugging in each of these so that f(x)=0. 

1: 1+10+14-6=19

-1: -1+10-14-6=-11

2: 8+40+28-6=70

-2: -8+40-28-6=-2

3: 27+90+42-6=153

-3: -27+90-42-6=15

6: 216+360+84-6=654

-6: -216+360-84-6=54

From this list, x=-2 is closest to an actual zero. None of the rational zeroes are actual zeroes.