Question

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

Dividend	Divisor
15y4 − 16y3 + 9y2 −\[\frac{10}{3}\] y+6	3y − 2

Answer 1

Quotient  = \[5 y^3 - 2 y^2 + \frac{5}{3}y\]

Remainder =  6
Divisor = 3y - 2 

Divisor x  Quotient + Remainder = (3y - 2) (5y³ - 2y² +

\[\frac{5}{3}y\]+ 6

\[15 y^4 - 6 y^3 + 5 y^2 - 10 y^3 + 4 y^2 - \frac{10}{3}y + 6\]

\[15 y^4 - 16 y^3 + 9 y^2 - \frac{10}{3}y + 6\]

 =  Dividend

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