Divide $(2 x^{3} + 3 x^{2} - 1)$ by $(x^{2} + 2 x + 1)$

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Solution

$(2 x^{3} + 3 x^{2} - 1) \div (x^{2} + 2 x + 1)$
$\frac{2 x^{3} + 3 x^{2} - 1}{x^{2} + 2 x + 1}$
$= \frac{(2 x - 1) (x^{2} + 2 x + 1)}{x^{2} + 2 x + 1}$
$= 2 x - 1$

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