help Factoring this equation

**^_^Engineer_Adam^_^** · February 3rd 2008, 01:26 AM

how do i factor this using synthetic division?
4x^4-16x^3+7x^2+4x-2 = 0

i will divide it by 2x - 1 but why?

after dividing it by 2x-1 i got a result of

2x^3 - 7x^2 + 2

i divide it by 2x+1 but why?

and i know this is trial and error
please help

**mr fantastic** · February 3rd 2008, 01:40 AM

Originally Posted by ^_^Engineer_Adam^_^

how do i factor this using synthetic division?
4x^4-16x^3+7x^2+4x-2 = 0

i will divide it by 2x - 1 but why?

after dividing it by 2x-1 i got a result of

2x^3 - 7x^2 + 2

i divide it by 2m+1 but why?

and i know this is trial and error
please help

Note that $4x^4-16x^3+7x^2+4x-2 = (4x^4-16x^3+8x^2) - x^2 +4x-2$

$= 4x^2 (x^2 - 4x + 2) - (x^2 - 4x + 2)$

$= (4x^2 - 1)(x^2 - 4x + 2)$

$= (2x - 1)(2x + 1)([x^2 - 4x + 4] - 2)$

$= (2x - 1)(2x + 1)([x - 2]^2 - 2)$

$= (2x - 1)(2x + 1)(x - 2 - \sqrt{2})(x - 2 + \sqrt{2}).$

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