I really don't understand how they factorise this:
y^4+y^2+1
Can anyone lend me a hand?
$\displaystyle y^4 + y^2 + 1$.
Make the substitution $\displaystyle x = y^2$ so that the expression becomes
$\displaystyle x^2 + x + 1$
$\displaystyle = x^2 + x + \left(\frac{1}{2}\right)^2 - \left(\frac{1}{2}\right)^2 + 1$
$\displaystyle = \left(x + \frac{1}{2}\right)^2 + \frac{3}{4}$.
This is not factorisable over the Reals.
where you're going to use z^2+z+1 to solve the equation.
@prove it:
I only was able to solve it through the calculator and it's factorisable, but I wanted to know the method. The answer was $\displaystyle (y^2+y+1)(y^2-y+1)$. A friend told me to use another equation similar to it which made it more confusing.