Answer
$(6,0,-15)$
Work Step by Step
We know that $a(5-3x)+b(1)+c(1+2x^2)=15-18x-30x^2$.
Thus $5a-3ax+b+c+2cx^2\\
=(5a+b+c)-3ax+2cx^2\\
=15-18x-30x^2$
Thus $5a+b+c=15\\ -3a=-18 \\ 2c=-30$
Thus $5.6+b-15=15 \\ a=6 \\ c=-15$
Thus $a=6 \\ b= 0 \\ c=-15$
Thus the vector is $(6,0,-15)$.
