Questions: Find the quotient using long division. 3x^3 + 2x^2 - 19x + 1 divided by x - 2

Solution Steps

Divide \(3 x^{3}\) by \(x\), resulting in \(3 x^{2}\). The remaining polynomial is \(8 x^{2} - 19 x + 1\).

Divide \(8 x^{2}\) by \(x\), resulting in \(8 x\). The remaining polynomial is \(1 - 3 x\).

Divide \(-3 x\) by \(x\), resulting in \(-3\). The remaining polynomial is \(-5\).

The quotient is \(3 x^{2} + 8 x - 3\) and the remainder is \(-5\).

The complete division expression is given by: \[ \frac{3 x^{3} + 2 x^{2} - 19 x + 1}{x - 2} = 3 x^{2} + 8 x - 3 - \frac{5}{x - 2} \]

Final Answer