$6 a^{2} - 13 a + 6 = ? (a) (2 a + 3) (3 a - 2) (b) (2 a - 3) (3 a + 2) (c) (3 a - 2) (2 a - 3) (d) (3 a + 1) (2 a - 3)$

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Solution

$6 a^{2} - 13 a + 6 = 6 a^{2} - 9 a - 4 a + 6 ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} ∵ 6 \times 6 = 36 ∴ 36 = (- 9) \times (- 4) - 13 = - 9 - 4 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ = 3 a (2 a - 3) - 2 (2 a - 3) = (2 a - 3) (3 a - 2)$

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