Find the quotient and remainder using synthetic division.

(3x³ – 4x² – 5) ÷ (3x + 1)

Let p(x) = 3x³ – 4x² – 5 be the dividend. Arranging p(x) according to the descending powers of x and insert zero for missing term.

p(x) = 3x³ – 4x² + 0x – 5

Divisor, q(x) = 3x + 1

⇒ To find out Zero of the divisor –

q(x) = 0

3x + 1 = 0

x =

zero of divisor is .

And, p(x) = 3x³ – 4x² + 0x – 5

Put zero for the first entry in the 2^nd row.

∵ p(x) = (Quotient)×q(x) + remainder.

So, 3x³ – 4x² – 5 = (x + )(3x² – 5x + ) + ()

= (3x + 1)(3x² – 5x + )

Thus, the Quotient = (3x² – 5x + )= (x² – x + ) and remainder is .

Hence, when p(x) is divided by (3x + 1) the quotient is (x² – x + ) and remainder is .