Question

Factorize:
$12 {x}^{2} - 7x - 1$
$2 {x}^{2} - x - 6 = 0$
$2 {x}^{2} - x + \frac{1}{8} = 0$
$100 {x}^{2} - 20x + 1 = 0$

Answer 1

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$(a)12x {}^{2} - 7x - 1 \\ = > 12x {}^{2} - 4x +3x - 1 \\ = > 4x(3x - 1) + 1(3x - 1) \\ = > (4x + 1)(3x -1 ) \\ \\ (b)2x {}^{2} - x - 6 \\ = > 2x {}^{2} - 4x + 3x - 6 \\ = > 2x(x - 2) + 3(x - 2) \\ = > (x - 2)(2x + 3) \\ \\ (c)2x {}^{2} - x + \frac{1}{8} \\ = > \frac{16x {}^{2} - 8x + 1 }{8} \\ = > 16x {}^{2} - 8x + 1 \\ = > 16x {}^{2} - 4x - 4x + 1 \\ = > 4x(4x - 1) - 1(4x - 1) \\ = > (4x - 1)(4x - 1) \\ \\ (d)100x {}^{2} - 20x + 1 \\ = > 100x {}^{2} - 10x - 10x + 1 \\ = > 10x(10x - 1) - 1(10x - 1) \\ = > (10x - 1)(10x - 1)$
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