Question
Find whether, or not the first polynomial is a factor of the second:
$\frac{10\text{a}^2-9\text{a}-5}{2\text{a}-3}$
$\frac{10\text{a}^2-9\text{a}-5}{2\text{a}-3}$
✓
Answer
$\frac{10\text{a}^2-9\text{a}-5}{2\text{a}-3}$
$=\frac{5 \text{a}(2\text{a}-3)(5\text{a}+3)+4}{2\text{a}-3}$
$=(5\text{a}+3)+\frac{4}{2\text{a}-3}$
Therefore, remainder $= 4$
$(2a - 3)$ is a factor of the factor of $10a^2 - 9a - 5$
$=\frac{5 \text{a}(2\text{a}-3)(5\text{a}+3)+4}{2\text{a}-3}$
$=(5\text{a}+3)+\frac{4}{2\text{a}-3}$
Therefore, remainder $= 4$
$(2a - 3)$ is a factor of the factor of $10a^2 - 9a - 5$
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