Question

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

Dividend	Divisor
6y5 + 4y4 + 4y3 + 7y2 + 27y + 6	2y3 + 1

Answer 1

Quotient = 3y² + 2y + 2

Remainder = 4y² + 25y + 4

Divisor = 2y³ + 1

Divisor x Quotient + Remainder = (2y³ + 1) (3y² + 2y + 2) + 4y² + 25y + 4

= 6y⁵ + 4y⁴ + 4y³ + 3y² + 2y + 2 + 4y² + 25y + 4

= 6y⁵ + 4y⁴ + 4y³ + 7y² + 27y + 6

 = Dividend

Thus,
Divisor x Quotient + Remainder = Dividend
Hence verified.