Question

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

Answer 1

ANSWER

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

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:

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