Question

The area of a rectangular art studio is given by the trinomial 12x^2 + 5x - 2 What are the

possible dimensions of the studio? Use factoring
​

Answer 1

Answer: (4x-1) and (3x-2)

took the test

- Iwasaki Katsuki

Answer 2

`(3x + 2) \: by \: (4x - 1)`

Step-by-step explanation

The area of a rectangular art studio is given by the quadratic trinomial:

`12{x}^(2) + 5x - 2`

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:

`12{x}^(2) + 8x - 3x- 2`

Factor by grouping,

`4x(3x + 2) - 1(3x + 2) = (3x + 2)(4x - 1)`

The possible dimensions are:

`(3x + 2) \: by \: (4x - 1)`