If $4\sqrt{3}x^2 + 5x - 2\sqrt{3} = (Ax +2) (Bx + C),$ then what is the value of (A + B + C) ? (A > 0)

4

Given,

4\(\sqrt {3}\) x² + 5x – 2\(\sqrt {3}\)  = (Ax + 2)(Bx + C)

According to the question,

4\(\sqrt {3}\) x² + 5x – 2\(\sqrt {3}\)

= 4\(\sqrt {3}\)x² + 8x – 3x – 2\(\sqrt {3}\)

= 4x(\(\sqrt {3}\) x + 2) – \(\sqrt {3}\) (\(\sqrt {3}\) x + 2)

= (\(\sqrt {3}\) x + 2) (4x – \(\sqrt {3}\))

Now,

⇒ A = \(\sqrt {3}\), B = 4 and C = -\(\sqrt {3}\)

(A + B + C) = (\(\sqrt {3}\)  + 4 + (-\(\sqrt {3}\))

= (\(\sqrt {3}\) + 4 – \(\sqrt {3}\))

= 4