1. [tex]x^2+5x+6 = (x+3)(x+2)[/tex], which implies that the sides could be [tex]x+3[/tex] and [tex]x+2[/tex]. (There are theoretically an infinite number of side-lengths, though--in general, for any polynomial or reciprocal of a polynomial [tex]P(x)[/tex], [tex]\frac{x+3}{P(x)}[/tex] and [tex]P(x)(x+2)[/tex] is valid. However, the set provided makes the most sense.)
2. Profit is the difference between cost and revenue. For revenue, [tex]0.0000x^2 = 0[/tex], so revenue equals [tex]40x[/tex], so profit equals [tex]26x-120,000.[/tex]
