Question

The area of a rectangle is x^2 - 2x - 15 and the length of the rectangle is x + 3. Find the width of the rectangle.

A. x – 5
B. x + 5
C. (x – 2)(x + 3)

Answer 1

The geometric expression for area of a rectangle is \(A_r = l w\) where \(l\) is the length and \(w\) is the width. If we substituted the given expression for area and length, we can solve for the expression of width.
\[ x^2 - 2x - 15 = w(x + 3) \] The basic interpretation of this is: "what polynomial for w when multiplied to (x+3) will get (x^2 - 2x - 15)?" We can either factor the right hand side or just use polynomial division. I personally think factoring is easier.

Answer 2

not the right hand, the left hand. Oh goodness, my direction skills. :P

Answer 3

Does that make sense, though? Are you able to take it from here?