Answer
The two dimensions are (x+2) and (x-24)
Work Step by Step
The area of a rectangle is $l \times w$ so given the area= $x^{2} -22x - 48$ we must factor them to find the l and w.
Given the polynomial
$x^{2} -22x - 48$
*** We break of the middle term into two factors that add to give -22 and multiply to give -48. The two numbers are -24 and +2.
$x^{2} -24x + 2x - 48$
We take the GCD of the first two and the GCD of the last two terms.
x(x-24) +2(x-24)
We take (x-24) and factor it out which gives us.
(x-24)(x+2)
Therefore since Area=$l \times w$ the two dimensions are (x+2) and (x-24)
