+6251 \(\mbox{We want to check factors of the constant term, 12, for possible roots.} \\ \mbox{1 and -1 are not roots.}\\ \mbox{2 is a root. So we can divide through by }(x-2)\\ \dfrac {2x^4-5x^3-11x^2+20x+12}{x-2}=2 x^3-x^2-13 x-6\\ \mbox{Now we look for roots of this polynomial from factors of 6.}\\ \mbox{Checking we find that -2 is a root so we can divide through by }(x+2)\\ \dfrac {2 x^3-x^2-13 x-6}{x+2}=2 x^2-5 x-3\)
\(\mbox{Again we look for roots from factors of the constant term 3.}\\ \mbox{We find 3 is a root so we can divide through by }(x-3)\\ \dfrac {2x^2-5x-3}{x-3}=2x+1 \\ \mbox{So the full factorization is }\\ 2 x^4-5 x^3-11 x^2+20 x+12 = (x+2)(x-2)(x-3)(2x+1)\)
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