Factorize $15 x^{2} - 26 x + 8$

(x -2)(x-4)

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(5x + 2) (3x -4)

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(5x + 2)(3x + 4)

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(5x -2)(3x -4)

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Solution

The correct option is D (5x -2)(3x -4)
Factors of $120 : 15 \times 8, 1 \times 120, 2 \times 60, 3 \times 40, 4 \times 30, 6 \times 20, 5 \times 24, 10 \times 12$
Suitable factors of 120 whose sum is -26 and product is 120 are 6 and 20. Since $(- 6) + (- 20) = - 26$ and $- 6 \times - 20 = 120$ , we have
$15 x^{2} - 26 x + 8 = 15 x^{2} - 6 x - 20 x + 8$
$= 3 x (5 x - 2) - 4 (5 x - 2)$
$= (5 x - 2) (3 x - 4)$

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