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Need help with factoring polynomials?
Okay, I know how to find the zeroes in a polynomial equation through synthetic division, but once I have one root and am left with factoring out the other roots, I'm lost.
Here's what I'm stuck with:
x^4-5x^3+20x-16=0
I found that +1 is a root, so I end up with
(x-1)(x^3-4x^2-4x+16)=0, then
(x-1)[x^2(x-4)-4(x-4)]=0
... Now what? In everything I look at, numbers just seem to disappear in the next step and it's just magically sorted and solved with no explanation, so I assume it's something simple that I'm just missing?
I'm still confused... When changing (x-1)[x^2(x-4)-4(x-4)]=0 to (x-1)(x-4)(x^2-4)=0, where does the second (x-4) go? The problem had the elements (x-1), (x-4), (x-4), and (x^2-4), right? Do the (x-4)'s cancel to one?
1 Answer
- ?Lv 69 years agoFavorite Answer
Well done, in my opinion. :-) So far you have:
(x-1)[x^2(x-4)-4(x-4)]=0
or
(x-1)(x-4)(x^2-4)=0
So, factor x^2 - 4 to get further.
(x-1)(x-4)(x-2)(x+2)=0
