Verify the division algorithm i.e., Dividend = Divisor × Quotient… - Vidyadip

Question

Verify the division algorithm i.e., Dividend = Divisor × Quotient + Remainder, in the following. Also write the quotient and remainder.
Dividend: $6 y^5+4 y^4+4 y^3+7 y^2+27 y+6$
Divisor: $2 y^3+1$

✓

Answer

$\text { Quotient }=3 y^2+2 y+2$
$\text { Remainder }=4 y^2+25 y+4$
$\text { Divisor }=2 y^3+1$
$\text { Divisor } \times \text { Quotient }+ \text { Remainder }=\left(2 y^2+1\right)\left(3 y^2+2 y+2\right)+4 y^2+25 y+4$
$=6 y^5+4 y^4+4 y^3+3 y^2+2 y+2+4 y^2+25 y+4$
$=6 y^5+4 y^4+4 y^3+7 y^2+27 y+6$
$=\text { Dividend }$
$\text { Divisor } \times \text { Quotient }+ \text { Remainder }=\text { Dividend }$
Hence verified.

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