Question

Find LCM of
${x}^{2} - 16 \: \: and \: 2 {x}^{2} - 9x + 4$
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Answer 1

Step-by-step explanation:

${x}^{2} - 16 \\ = {x}^{2} - {4}^{2} = (x + 4)(x - 4) \\ \\ 2 {x}^{2} - 9x + 4 \\ = 2 {x}^{2} - 8x - x + 4 \\ = 2x(x - 4) - 1(x - 4) \\ = (x - 4)(2x - 1) \\\\Now, LCM \: of \: ({x}^{2} - 16 )\: and \: \\ (2 {x}^{2} - 9x + 4)\\ = common \: factors \times uncomon \: factors \\ = (x - 4)(x + 4)(2x - 1) \\ = ( {x}^{2} - 16)(2x - 1)$