Question

A piece of cloth is folded into a square with a side length measuring x inches. When it is unfolded, it has an area of x2 + 27x + 162 square inches. Which could be the dimensions of the rectangular piece of cloth when it is unfolded? Remember, the area of a rectangle can be determined using the formula A = lw.

A).length = (x + 9) inches and width = (x + 3) inches
B).length = (x − 3) inches and width = (x − 9) inches
C).length = (x + 18) inches and width = (x + 9) inches
D).length = (x − 9) inches and width = (x − 18) inches

Answer 1

Our task here is to find possible factors of x^2 + 27x + 162.
We need to check out possible factors of 162 first.  Examples are:
2(81), 3(54), 6(27), 9(18), and so on.  Notice that 9 and 18 add up to 27, so that the factors (x+9) and (x+18) produce x^2 + 27x + 162 when mult. together.