If the values matched, I would be fairly confident in my answer. I wanted a different way to check that my answer was correct.Įventually, I realized that all I had to do was pick a value of x and substitute it into the original question and the answer x³ - 6x² - x + 30. Checking each step was tedious and prone to error-I knew too well that I would probably be blind to errors in the work I had just written. If a teacher asked me to calculate the expanded form of the polynomial (x + 2)(x - 3)(x - 5), I had to carry out multiple arithmetic steps before I arrived at an answer. In fact, most of the tricks I rediscovered were motivated by a simple academic need: Was my answer correct or not? Indeed, while I didn’t know it at the time, this question would become the fundamental basis for my internship at Galois this summer.Īt about the time I started learning algebra, I began to notice that my tricks for checking arithmetic had become insufficient. It wasn’t until much later that I discovered that this was a very rudimentary form of the checksum. I was (and still am) very sloppy when it came to pencil-and-paper arithmetic-if I didn’t check my answers, I would invariably lose points because of “stupid mistakes.” Fortunately, I knew the following trick: if I summed together the digits of my factors (re-summing if the result was ten or more), the product of these two numbers should match the sum of the digits of the result. I can recall taking a math quiz-calculators banned-facing a difficult task: the multiplication of large numbers.

As a high schooler, I was using concepts from computer science long before I even knew what computer science was. What I did for my summer internship at Galois

Simple algebra quiz