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Division of Algebraic Expressions — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsDivision of Algebraic Expressions4 Marks
Question
Find whether, or not the first polynomial is a factor of the second:
$\frac{3\text{y}^3+5\text{y}^2+5\text{y}+2}{\text{y}-2}$
✓

Answer

$\frac{3\text{y}^3+5\text{y}^2+5\text{y}+2}{\text{y}-2}$
$=\frac{3\text{y}^2(\text{y}-2)+11\text{y}+27(\text{y}-2)+56}{\text{y}-2}$
$=\frac{(\text{y}-2)\big(3\text{y}+11\text{y}+27\big)+56}{\text{y}-2}$
$=\Big(3\text{y}^2+11\text{y}+27\Big)+\frac{56}{\text{y}-2}$
$=\Big(3\text{y}^2+11\text{y}+27\Big)+\frac{56}{\text{y}-2}$
Therefore, $(y-2)$ is not a factor of $3 y^3+5 y^2+5 y+2$

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