Question

zoe is designing a rectangular garden. the area of the garden is given by the expression (2b^2 + 5b + 3) square meters. what could be the possible dimensions of the garden?
(2b - 1) meters by (b - 3) meters
(2b + 3) meters by (b + 1) meters
not factorable
(2b + 1) meters by (b + 3) meters

Explanation:

Step1: Factor the quadratic expression

We factor $2b^2 + 5b + 3$. We look for two binomials of the form $(mb + n)(pb + q)$ where $mp=2$, $nq=3$, and $mq+np=5$.
Testing $m=2$, $p=1$, $n=3$, $q=1$:
$mq + np = (2)(1) + (3)(1) = 2 + 3 = 5$, which matches.
So $2b^2 + 5b + 3 = (2b+3)(b+1)$

Step2: Match to dimension options

The area of a rectangle is length $\times$ width, so the dimensions are the factors of the area expression.

Answer:

B. (2b+3) meters by (b+1) meters