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

Question

Verify the division algorithm i.e., Dividend = Divisor $\times $ Quotient + Remainder, in the following. Also write the quotient and remainder.
Dividend: $4y^3+ 8y + 8y^2+ 7$
Divisor: $2y^2- y + 1$

✓

Answer

$ \text { Quotient }=2 y+5 $
$ \text { Remainder }=11 y+2 $
$ \text { Divisor }=2 y^2-y+1 $
$\text { Divisor } \times \text { Quotient }+ \text { Remainder }=\left(2 y^2-y+1\right)(2 y+5)+11 y+2 $
$=4 y^3+10 y^2-2 y^2-5 y+2 y+5+11 y+2 $
$ =4 y^3+8 y^2+8 y+7 $
= Dividend
Divisor × Quotient + Remainder = Dividend
Hence verified.

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