Question

1. A rectangle has an area given by A=x^2+5x+6. Find expressions for the possible lengths and width of the rectangle.

Answer 1

1.  $x^2+5x+6 = (x+3)(x+2)$, which implies that the sides could be $x+3$ and $x+2$.  (There are theoretically an infinite number of side-lengths, though--in general, for any polynomial or reciprocal of a polynomial $P(x)$, $\frac{x+3}{P(x)}$ and $P(x)(x+2)$ is valid.  However, the set provided makes the most sense.)

2.  Profit is the difference between cost and revenue.  For revenue, $0.0000x^2 = 0$, so revenue equals $40x$, so profit equals $26x-120,000.$