Answer
$6z^2+2z+\frac{11}{2}$
Work Step by Step
$(z^2+5)-(3z^2-1)+(8z^2+2z-\frac{1}{2})=(z^2+5)+(-3z^2+1)+(8z^2+2z-\frac{1}{2})$
$(z^2-3z^2+8z^2)+2z+(5+1-\frac{1}{2})=6z^2+2z+\frac{11}{2}$
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