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Question
Find whether the first polynomial is a factor of the second.
y − 2, 3y3 + 5y2 + 5y + 2
Solution
\[\frac{{3y}^3 {+5y}^2 +5y+2}{y-2}\]
\[ = \frac{{3y}^2 (y-2)+11y(y-2)+27(y-2)+56}{y-2}\]
\[ = \frac{{(y-2)(3y}^2 +11y+27)+56}{y-2}\]
\[ {=(3y}^2 +11y+27)+ \frac{56}{y-2}\]
\[ \because \text{Remainder} = 56\]
\[ \therefore \text{(y-2) is not a factor of}\ {3y}^3 {+5y}^2 +5y+2.\]
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