I want to show, that $X^4-4X^2-1$ is irreducible over $\mathbb{Q}[X]$. Since there are no roots in $\mathbb{Q}$ it has to be: $(X^4-4X^2-1)=(X^2+aX+b)(X^2...

After reading this question, the most popular answer use the identity $$\sum_{t=0}^n \binom{t}{k} = \binom{n+1}{k+1}.$$ What's the name of this ident...

Let's say we had a $n$th degree polynomial equation $a_{n}x^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\cdots+a_2x^2+a_1x+a_0=0$, with $a$ being real coefficien...

Is it true that the surface integral over any closed surface (we are in $\mathbb R^3$) of the normal vector $\hat n$ of that surface, say $\hat n$ is poin...

In part (a), I calculated that s(t) = $\int_0^t \! (\frac{t^2}{2} + 2t) \, \mathrm{d}t$ = $t^2/2 + 2t$ I'm unsure how to solve part (b). My attempt i...

How can I prove this? Should I take $x$ and $x+2$ or not ? I am confused.

I'm trying to solve the following equation $2t^2 + t - 3 = 0$ I start by dividing by 2, $t^2 + \frac {t}{2} - \frac {3}{2} = 0$ Then I solve for t $t...

If I know that, in a rhombicosidodecahedron, at every vertex one triangle, one pentagon, and two squares meet, then how can I compute the number of faces ...

My son's homework sheet says to solve problems like: (5) / (15/4) and to write the "quotient" in its "simplest" form. The crux of my question is, whi...

I understand that a complex number $n = a + bi$ is defined as having real $a,b$ with $i = \sqrt{-1}$. However what I don't understand is the why. Why...