If the HCF of the expressions (x + 3) (2x² – 3x + a) and (x – 2) (3x² + 10x – b) is x² + x – 6, then what is the value of (2a – 3b) ?

Correct option is B

​$$\textbf{Given:} \\(x+3)(2x^2 - 3x + a),\quad (x-2)(3x^2 + 10x - b) \\\text{HCF} = x^2 + x - 6 \\\textbf{Concept Used:} \\\text{Common factors and factor theorem} \\\textbf{Formula Used:} \\x^2 + x - 6 = (x+3)(x-2) \\\textbf{Solution:} \\x^2 + x - 6 = (x+3)(x-2) \\\text{For first expression:} \\2x^2 - 3x + a \text{ divisible by } (x-2) \\2(2)^2 - 3(2) + a = 0 \\8 - 6 + a = 0 \\a = -2 \\\text{For second expression:} \\3x^2 + 10x - b \text{ divisible by } (x+3) \\3(-3)^2 + 10(-3) - b = 0 \\27 - 30 - b = 0 \\b = -3 \\2a - 3b = 2(-2) - 3(-3) \\= -4 + 9 \\= 5 \\\textbf{Final Answer:} \\5$$​​