Answer: (x-2)
Step-by-step explanation:
This problem is a middle-term factorization, or factoring by splitting the middle term.
We have the equation
x^2 - 18x + 32
This equation represents the area, and area = length x width for all rectangles. We also know the width, x-16, which makes it easier for us. The length must also be in the same format.
x^2 - 18x + 32
= x^2 - 16x - 2x + 32
= x(x-16) - 2(x - 16)
= (x-16) (x-2) -------> we get this through taking (x-16) common
We could also pretend that the length is x - y, where y is the number we need to finish the equation.
x^2 - 18x + 32
= (x-16) (x-y)
= x^2 -16x - xy + 16y
-16 minus 2 is -18, which is our middle term.
Therefore, y = 2. This is also verified because is 16y = 32, the constant term, then through transposing we get y = 2.
Our answer is that the length is (x-2).
