1. Factoring using 0

Here is a trick to factor x^3 + 1

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

2. Re: Factoring using 0

Try multiplication using Unity! Both very useful techniques.

3. Re: Factoring using 0

Is the OP asking a question?

4. Re: Factoring using 0

Originally Posted by agentmulder
Here is a trick to factor x^3 + 1

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
Hiii Agentredlum ! Good to see you here !
x^3+1 is an identity a^3+b^3
So
it will be
(x+1)(x^2+1-x)

5. Re: Factoring using 0

Hello there sankalpmittal, I guess my point is that it is possible to use 'nothing' to get 'something'

I LOVE your circle area derivation, I am very impressed.:smile:

6. Re: Factoring using 0

Originally Posted by agentmulder
Hello there sankalpmittal, I guess my point is that it is possible to use 'nothing' to get 'something'

I LOVE your circle area derivation, I am very impressed.:smile:
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.