Mr. smith is unhappy with the 2 foot concrete walkway around the edge of the pool. he decides to put a different width around the pool. the total area of the pool and the walkway is given by the polynomial w^2 + 17w + 66

Given that the total area of the walkway and the pool is w²+17w+66, and the width w, will be found as follows:
A=length×width
A=w²+17w+66
to get the new width we need to factorize the above quadratic form
A=w²+17w+66
=w²+11w+6w+66
=w(w+11)+6(w+11)
=(w+11)(w+6)
From the answer, the width=6 units, length=11 units

Welp life just is hard