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Division of Algebraic Expressions — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsDivision of Algebraic Expressions3 Marks
Question
Divide the first polynomial by the second polynomial in the following. Also write the quotient and remainder:
$\frac{\big(\text{y}^4+\text{y}^2\big)}{\text{y}^2-2}$
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Answer

$\frac{\big(\text{y}^4+\text{y}^2\big)}{\text{y}^2-2}$
$=\frac{\text{y}^2\big(\text{y}^2-2\big)+3\big(\text{y}^2-2\big)+6}{\text{y}^2-2}$
$=\frac{\big(\text{y}^2-2\big)\big(\text{y}^2+3\big)}{\text{y}^2-2}$
$=\big(\text{y}^2+3\big)+\frac{6}{\text{y}^2-2}$
Therefore, quotient $= y ^3+3$ and remainder $=6$

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