ANSWER
[tex](3x + 2) \: by \: (4x - 1)[/tex]
EXPLANATION
The area of a rectangular art studio is given by the quadratic trinomial:
[tex] 12{x}^{2} + 5x - 2[/tex]
By comparing this to:
ax²+bx+c
We have a=12, b=5, and c=-2
ac=12*-2=-24
The factors of -24 that gives a sum of 5 are 8,-5
We split the middle term with these factors to get:
[tex]12{x}^{2} + 8x - 3x- 2[/tex]
Factor by grouping,
[tex]4x(3x + 2) - 1(3x + 2) = (3x + 2)(4x - 1)[/tex]
The possible dimensions are:
[tex](3x + 2) \: by \: (4x - 1)[/tex]
