Question
Divide $15\text{y}^4+16\text{y}^3+\frac{10}{3}\text{y}-9\text{y}^2-6\text { by }3\text{y}-2.$ Write down the coefficients of the terms in the quotient.
✓
Answer
$\therefore$ Quotient $=5\text{y}^3+\Big(\frac{26}{3}\Big)\text{y}^2+\Big(\frac{25}{9}\Big)\text{y}+\Big(\frac{80}{27}\Big)$
Remainder $=\Big(\frac{-2}{27}\Big)$
Coefficient of $\text{y}^3=5$
Coefficient of $\text{y}^2=\Big(\frac{26}{3}\Big)$
Coefficient of $\text{y}=\Big(\frac{25}{9}\Big)$
Constant $=\Big(\frac{80}{2}\Big)$
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