# Difference of two squares considered to be a quadratic

1. Aug 20, 2011

### vanmaiden

1. The problem statement, all variables and given/known data
is an expression that is a difference of two squares considered to be a quadratic. For example, would x2 - 4 be a quadratic? What about x4 - 4?

2. Relevant equations
Ax2 + Bx + C

3. The attempt at a solution
I know we can factor a DOTS into two binomials like a quadratic in the for Ax2 + Bx + C, but I wanted to be clear on what a DOTS was relative to a quadratic equation.

2. Aug 20, 2011

### HallsofIvy

Staff Emeritus
Re: Dots

"Quadratic" simply means "a polynomial of degree 2". Yes, $x^2- 4$ is quadratic, no, $x^4- 4$ is not. The importance of the "difference of two squares" is, as you say, that it can be easily factored: the quadratic $x^2- 4$ can be factored into two linear factors: $(x- 2)(x+ 2)$, the quartic $x^4- 4$ can be factored into two quadratic terms: $(x^2- 2)(x^2+ 2)$.

3. Aug 24, 2011

### vanmaiden

Re: Dots

So, to be clear, x4 - 4 is a quartic. Is there a special name given to something like x6 - 4?

4. Aug 24, 2011

### Staff: Mentor

Re: Dots

I haven't seen any terminology for polynomials higher than degree five, and these are called quintics.

5. Aug 24, 2011

### vanmaiden

Re: Dots

Interesting. I'll be on the lookout