# Category Archives: Algebra

I was trying to solve an olympiad type problem involving a nested radical of the form $\sqrt{a+b\sqrt{r}}.$ I had managed to discover that $\sqrt{a^2- b^2r}$ is an integer but it turned out the trick is to rewrite … Continue reading

## Polynomial Puzzle and Lill’s Method

I have in mind a polynomial with nonnegative integer coefficients. Can you determine completely the polynomial by just asking two questions? I forgot where I saw this from but it was interesting enough to spur a few lunch time discussions … Continue reading

## Magic formula

Was grading some student work and noticed that when they are supposed to solve for $\left(\frac{5y}{4}-\frac{1}{2}\right)^2 +\frac{1}{16} = 1$, 10 out of 16 students expanded the above into a quadratic equation and then used the quadratic formula to get … Continue reading

Posted in Algebra, Teaching | 2 Comments

## Why is ‘x’ the unknown?

A short 4 min video explains …

In the midst of grading exams now. One problem consists of computing determinants and many students give the answer $(1+a)^3 -3a -1$ without simplifying it to $a^3+3a^2$. I have this nagging suspicion that they are not … Continue reading