We #160;have #160;3x2 #160; #160;5x2 #160; #160;2x2 #160; #160;5x #160;+ #160;5 #160; #160;6.Let #160;x2 #160; 5x= #160;a #8 ...

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3x2-5 x2-2x2-...

Question

3(x² $-$ 5x)² $-$ 2(x² $-$ 5x + 5) $-$ 6

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Solution

$We have 3 {(x^{2} - 5 x)}^{2} - 2 (x^{2} - 5 x + 5) - 6 . Let x^{2} - 5 x = a ∴ 3 {(x^{2} - 5 x)}^{2} - 2 (x^{2} - 5 x + 5) - 6 = 3 a^{2} - 2 (a + 5) - 6 = 3 a^{2} - 2 a - 16 = 3 a^{2} - 8 a + 6 a - 16 = a (3 a - 8) + 2 (3 a - 8) = (3 a - 8) (a + 2) Resubstituting the value of a, we get : 3 {(x^{2} - 5 x)}^{2} - 2 (x^{2} - 5 x + 5) - 6 = [3 (x^{2} - 5 x) - 8] [(x^{2} - 5 x) + 2] = (3 x^{2} - 15 x - 8) (x^{2} - 5 x + 2)$

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