Try multiplication using Unity! Both very useful techniques.
Here is a trick to factor x^3 + 1
subtract x and add x
1) x^3 - x + x + 1
group
2) (x^3 - x) + (x +1)
factor
3) x(x^2 - 1) + (x + 1)
4) x(x - 1)(x + 1) + (x + 1)
5) (x + 1)[x(x -1) + 1]
6) (x + 1) (x^2 - x + 1)
The same clever use of 0 can help you factor x^3 - 1
Clever use of 0 can help you factor x^4 + x^2 + 1 by subtracting and adding x
1) x^4 + x + x^2 - x + 1
group
2) (x^4 + x) + (x^2 - x + 1)
factor
3) x(x^3 + 1) + (x^2 - x + 1)
4) x(x +1)(x^2 - x + 1) + (x^2 - x + 1)
5) (x^2 - x + 1)(x^2 + x + 1)
Many other factorizations are possible using 0
May I know why were you banned from physics forums ? Just because your quadratic formula was different from textbook definition ?!
We will also prove that whether your formula is right . Just ask Dr. Math , he is a genius in mathematics. Ask him here : The Math Forum: Write to Dr. Math
If he agrees that your formula is well simplified from textbook definition , then rest of the forum members must confess.
Dr. Math will reply in your id within 1 day.
Cheers !