Question
Verify the division algorithm i.e., Dividend = Divisor × Quotient + Remainder, in the following. Also write the quotient and remainder.
Dividend: $4 y^3+8 y+8 y^2+7$
Divisor: $2 y^2-y+1$
Dividend: $4 y^3+8 y+8 y^2+7$
Divisor: $2 y^2-y+1$
✓
Answer
Quotient $= 2y + 5$
Remainder $= 11y + 2$
Divisor $= 2 y^2-y+1$
Divisor × Quotient + 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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