$$\Delta $$ = $$\left| {\matrix{ {x - 2} & {2x - 3} & {3x - 4} \cr {2x - 3} & {3x - 4} & {4x - 5} \cr {3x - 5} & {5x - 8} & {10x - 17} \cr } } \right|$$

R₂ $$ \to $$ R₂ – R₁
R₃ $$ \to $$ R₃ – R₂

= $$\left| {\matrix{ {x - 2} & {2x - 3} & {3x - 4} \cr {x - 1} & {x - 1} & {x - 1} \cr {x - 2} & {2\left( {x - 2} \right)} & {6\left( {x - 2} \right)} \cr } } \right|$$

= $$\left( {x - 1} \right)\left( {x - 2} \right)\left| {\matrix{ {x - 2} & {2x - 3} & {3x - 4} \cr 1 & 1 & 1 \cr 1 & 2 & 6 \cr } } \right|$$

C₁ $$ \to $$ C₁ - C₂
C₂ $$ \to $$ C₂ - C₃

= $$\left( {x - 1} \right)\left( {x - 2} \right)\left| {\matrix{ { - x + 1} & { - x + 1} & {3x - 4} \cr 0 & 0 & 1 \cr { - 1} & { - 4} & 6 \cr } } \right|$$

= -(x - 1)(x - 2)[-4(1 - x) + 1(1 - x)]

= -(x² - 3x + 2)[3x - 3]

= -3x³ + 9x² - 6x + 3x² - 9x + 6

= -3x³ + 12x² - 15x + 6 = Ax³ + Bx² + Cx + D

$$ \therefore $$ A = -3, B = 12, C = -15

$$ \therefore $$ B + C = 12 – 15 = – 3