Find the quotient and remainder using synthetic division.

(8x⁴ – 2x² + 6x + 5) ÷ (4x + 1)

Let p(x) = 8x⁴ – 2x² + 6x – 5 be the dividend. Arranging p(x) according to the descending powers of x and insert zero for missing term.

p(x) = 8x⁴ + 0x³ – 2x² + 6x – 5

Divisor, q(x) = 4x + 1

⇒ To find out Zero of the divisor –

q(x) = 0

4x + 1 = 0

x =

zero of divisor is .

And, p(x) = 8x⁴ + 0x³ – 2x² + 6x – 5

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

∵ p(x) = (Quotient)×q(x) + remainder.

So, 8x⁴ – 2x² + 6x – 5 = (x + )( 8x³ – 2x² – x + ) + ()

= (4x + 1)(8x³ – 2x² – x + )

Thus, the Quotient = (8x³ – 2x² – x + )= (2x³ – x² – x + ) and remainder is .

Hence, when p(x) is divided by (4x + 1) the quotient is (2x³ – x² – x + ) and remainder is .