AHSME 1969 Problem 12

Let $F=\frac{6x^2+16x+3m}{6}$ be the square of an expression which is linear in $x$. Then $m$ has a particular value between: $\text{(A) } 3 \text{ and } 4 \text{(B) } 4 \text{ and } 5 \text{(C) } 5 \text{ and } 6 \text{(D) } -4 \text{ and } -3 \text{(E) } -6 \text{ and } -5$