I need help on how to factorize the following w/o calculator if possible.

I've attempted to factor with whole numbers with no avail.

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- March 30th 2010, 12:24 AMCthul[Factorization] Factorization of polynomials
I need help on how to factorize the following w/o calculator if possible.

I've attempted to factor with whole numbers with no avail. - March 30th 2010, 01:56 AMHallsofIvy
- March 30th 2010, 02:11 AMCthul
Okay.

I've checked the answers and the factor of it is.

For the solution to be true

From what I know, via the answers.

Has no solutions because

Then there are no solutions.

So, is there no way to do this mentally or by hand? Assuming I am factorizing over irrational numbers. - March 30th 2010, 02:58 AMmr fantastic
HOI reasonably assumed that you wanted linear factors.

Since linear factors involving integers are not possible, it's natural to then try to factor it as a product of two quadratics:

(x^2 + ax + b)(x^2 + cx + d)

and then see if you can find integer values of a, b, c and d. - March 30th 2010, 03:16 AMCthul
Oh, I see. Thanks.

- April 1st 2010, 06:28 PMCthul
I'm still stuck on this equation. I tried factorizing by identical equations but I end up with too many variables, is there really no way to factor this? I want to know how to factorize this.

(My attempt to factorize)

The identity?

Expanded.

Common Factor.

So

Original Equation:

- April 8th 2010, 11:18 PMCthul
So does anyone have a method to solve this?

- April 8th 2010, 11:57 PMmr fantastic
- April 8th 2010, 11:58 PMCthul
It's an exercise from the book, and the section specified that calculators are not to be used.

- April 9th 2010, 12:15 AMBacterius
Hello,

you might want to solve the system for and , thus recovering the factorized expression of the polynomial and solving it in the standard way.

However I don't know if it is possible to solve this system. You have four unknowns and four equations, but how to solve it I have no idea yet (haven't really looked). Try to work out some algebra around the system and see what you can do ?