Factorize the following:
$(3 x - 2 y)^{2} + 3 (3 x - 2 y) - 10$

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

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(3 x - 8 y + 5) (x - 2 y - 2)

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

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

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Solution

The correct option is B $(3 x - 2 y + 5) (3 x - 2 y - 2)$
$(3 x - 2 y)^{2} + 3 (3 x - 2 y) - 10$
$= (3 x - 2 y)^{2} + 5 (3 x - 2 y) - 2 (3 x - 2 y) - 10$
$= (3 x - 2 y) (3 x - 2 y + 5) - 2 (3 x - 2 y + 5)$
$= (3 x - 2 y + 5) (3 x - 2 y - 2)$

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\frac{1}{2 (x + 2 y)} + \frac{5}{3 (3 x - 2 y)} = \frac{- 3}{2}

\frac{5}{4 (x + 2 y)} - \frac{3}{5 (3 x - 2 y)} = \frac{61}{60}

(3 x - 2 y)^{2} + 3 (3 x - 2 y) - 10

z = 5 x + 2 y

x - 2 y \leq 2

3 x + 2 y \leq 12

- 3 x + 2 y \leq 3

x \geq 0, y \geq 0

z = 5 x + 2 y

x - 2 y \leq 2

3 x + 2 y \leq 12

- 3 x + 2 y \leq 3

x \geq 0, y \geq 0

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