Find the quotient and remainder using synthetic division.

(3x³ + 4x² – 10x + 6) ÷ ( 3x – 2)

Let p(x) = 3x³ + 4x² – 10x + 6 be the dividend and arranging p(x) according to the descending powers of x.

Divisor, q(x) = 3x – 2

⇒ To find out Zero of the divisor –

q(x) = 0

3x – 2= 0

x =

So, zero of divisor is .

And, p(x) = 3x³ + 4x² – 10x + 6

Put zero for the first entry in the second row.

∵ p(x) = (Quotient)×q(x) + remainder.

So, 3x³ + 4x² – 10x + 6 = (x – )(3x² + 6x – 6) + 2

= (3x – 2)(3x² + 6x – 6) + 2

Thus, the Quotient = (3x² + 6x – 6)= x² + 2x – 2 and remainder is 2.

Hence, when p(x) is divided by (3x – 2) the quotient is x² + 2x – 2 and remainder is 2.