Question

Find the remainder when the polynomial $4y^3-3y^2-5y+1$ is divided by $2y+3$.

Answer 1

$2y+3$ $)4y^3-3y^2-5y+1($ $2y^2-\frac{9}{2}y+\frac{17}{4}$

$4y^3+6y^2$

$(-)$

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$-9y^2-5y$

$-9y^2-\frac{27}{2}y$

$(-)$

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$\frac{17}{2}y+1$

$\frac{17}{2}y+\frac{51}{4}$

$(-)$

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$-\frac{47}{4}$

$\frac{4y^3-3y^2-5y+1}{2y+3}=2y^2-\frac{9}{2}y+\frac{17}{4}-\frac{47}{4(2y+3)}$