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Oh boy time to factor some quadratics

Source: 1959 AHSME Problem 16

August 13, 2013
quadraticsAMCfactoring quadraticsAMC 12algebra

Problem Statement

The expression x2−3x+2x2−5x+6÷x2−5x+4x2−7x+12\frac{x^2-3x+2}{x^2-5x+6}\div \frac{x^2-5x+4}{x^2-7x+12}, when simplified is: <spanclass=′latex−bold′>(A)</span> (x−1)(x−6)(x−3)(x−4)<spanclass=′latex−bold′>(B)</span> x+3x−3<spanclass=′latex−bold′>(C)</span> x+1x−1<spanclass=′latex−bold′>(D)</span> 1<spanclass=′latex−bold′>(E)</span> 2 <span class='latex-bold'>(A)</span>\ \frac{(x-1)(x-6)}{(x-3)(x-4)} \qquad<span class='latex-bold'>(B)</span>\ \frac{x+3}{x-3}\qquad<span class='latex-bold'>(C)</span>\ \frac{x+1}{x-1}\qquad<span class='latex-bold'>(D)</span>\ 1\qquad<span class='latex-bold'>(E)</span>\ 2
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