Question 1043537
<font color=black size=3>x+1 is equivalent to x-(-1)



x-(-1) is in the form x-k where k = -1



So we'll plug x = -1 into P(x) to get



{{{P(x) = 3x^3+a*x-2}}}



{{{P(-1) = 3(-1)^3+a*(-1)-2}}} Replace every x with -1



{{{P(-1) = 3(-1)+a*(-1)-2}}}



{{{P(-1) = -3-a-2}}}



{{{P(-1) = -a-3-2}}}



{{{P(-1) = -a-5}}}



Now replace P(-1) with 2. Why 2? Because this is the remainder. I'm using the remainder theorem.



{{{P(-1) = -a-5}}}



{{{2 = -a-5}}} Replace P(-1) with 2



Now we solve for 'a'



{{{2 = -a-5}}}



{{{2+a = -a-5+a}}} Add 'a' to both sides



{{{2+a = -5}}}



{{{a+2 = -5}}}



{{{a+2-2 = -5-2}}} Subtract 2 from both sides



{{{a = -7}}}



So the final answer is <font color=red size=4>choice A) -7</font>
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