Question 970481: I am trying to factor this problem but i'm stumped can you help me? Here is the problem:
x^5-7x^3+4x^2-28. I don't see any common factors so I'm stuck.
I first tried to do -7x^3+4x^2= -3x. I put this into the equation x^5-3x-28 I don't think this is right.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! The polynomial might be factorable by grouping, but seeing it is a polynomial with so many (only four ) terms, Rational Roots Theorem, Factor and Remainder Theorems might be helpful.
But back to grouping, see the 4 and the 28; or see the -7 and the -28. You might try separating them, but the feeling here is that such grouping may lead to nothing useful. You could still try.
My better impulse is to try testing "roots" of -1, -2, -4, -7, -14, 1, 2, 4, 7, 14, according to Rational Roots Theorem. Do you know how to do polynomial division? You could try dividing your degree-five polynomial by (x+1), (x+2), (x+4), and so on according to the listed possible roots. Remainder of 0 means you found a root (or a factor of your polynomial).
Be sure to use the polynomial you were given as this:
 , as the dividend to start with.
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After trying with different divisions, mostly synthetic division for checking possible roots, I found nothing.
If you arrange your given polynomial like this:  ,
you can form this:  . Not the neatest result, but somewhat factored.
Answer by MathTherapy(10555)  (Show Source):
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