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Division of Algebraic Expressions — MATHS STD 8 — Question

Gujarat 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:
$\frac{5\text{y}^3-6\text{y}^2+6\text{y}-1}{5\text{y}-1}$
✓

Answer

$\frac{5\text{y}^3-6\text{y}^2+6\text{y}-1}{5\text{y}-1}$
$=\frac{\text{y}^2(5\text{y}-1)-\text{y(5}\text{y}-1)+1(5\text{y}-1)}{5\text{y}-1}$
$=\frac{(5\text{y}-1)\big(\text{y}^2-\text{y}+1\big)}{5\text{y}-1}$
$\text{y}^2-\text{y}+1+5$
Therefore, quotient $= y^2 - y + 1$ and remainder $= 0$

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