Find whether, or not the first polynomial is a factor of the seco… - Vidyadip

Question

Find whether, or not the first polynomial is a factor of the second:
$\frac{8\text{y}^2-2\text{y}+1}{4\text{y}+1}$

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Answer

$\frac{8\text{y}^2-2\text{y}+1}{4\text{y}+1}$
$=\frac{2\text{y(4}\text{y+1)}-1(4\text{y}+1)+2}{4\text{y}+1}$
$=\frac{(4\text{y}+1)(2\text{y}-1)+2}{4\text{y}+1}$
$=2\text{y}-1+\frac{2}{4\text{y}+1}$
$=\frac{\text{x}^2-5\text{x}+6}{\text{x}-3}$
$=\frac{\text{x}^2-3\text{x}-2\text{x}+6}{\text{x}-3}$
$=\frac{\text{x}(\text{x}-3)-2(\text{x}-2)}{\text{x}-3}$
$=\frac{(\text{x}-3)(\text{x}-2)}{\text{x}-3}=\text{x}-2$
Therefore, remainder = 2
$(4 y+1)$ is not a factor of $8 y^2-2 y+1$

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