Question 144118
You have identified all of the possible rational zeros.  Only 2 of them are represented in your set of answers, so you only have to check those two.  Remember that if {{{a}}} is a zero, then {{{f(a)=0}}}


{{{f(x) = 3x^4 - 11x^3 + 10x - 4}}}
{{{f(1) = 3(1)^4 - 11(1)^3 + 10(1) - 4=3-11+10-4=-2}}}.  Therefore not a zero
{{{f(-1) = 3(-1)^4 - 11(-1)^3 + 10(-1) - 4=3+11-10-4=0}}}.  Therefore -1 is a zero.


Answer d.


Super Double Plus Extra Credit:
Are there any other rational zeros?  Hint: Use polynomial long division or synthetic division to divide {{{f(x)}}} by {{{x+1}}}.  Remember to include {{{0x^2}}} as a place holder.  Repeat use of the Rational Zero Theorem to find any zeros for the 3rd degree polynomial quotient.