Question

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

Dividend	Divisor
4y3 + 8y + 8y2 + 7	2y2 − y + 1

Answer 1

Quotient =  2y + 5
Remainder =  11y + 2
Divisor =  2y² -  y + 1

Divisor x Quotient + Remainder =  (2y² - y + 1) (2y + 5) + 11y + 2

 =  4y³ +10y² -  2y² - 5y + 2y + 5 + 11y + 2

=  4y³ + 8y² + 8y + 7

=  Dividend

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