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Division of Algebraic Expressions — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSDivision of Algebraic Expressions5 Marks
Question
Verify the division algorithm i.e., Dividend = Divisor $\times $ Quotient + Remainder, in the following. Also write the quotient and remainder.
Dividend: $6y^5+ 4y^4+ 4y^3+ 7y^2+ 27y + 6$
Divisor: $2y^3+ 1$
✓

Answer



Quotient $= 3y^2+ 2y + 2$
Remainder $= 4y^2+ 25y + 4$
Divisor $= 2y^3+ 1$
Divisor $\times $ Quotient + Remainder $= (2y^2+ 1)(3y^2+ 2y + 2) + 4y^2+ 25y + 4$
$ =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 $
= Dividend
Divisor $\times $ Quotient + Remainder = Dividend
Hence verified.

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