Divide $$ \left(2 x^{3}+3 x^{2}-4 x+15\right) $$ by $$ (x+3) $$ using synthetic division

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The result of dividing $$ 2x^3 + 3x^2 - 4x + 15 $$ by $$ x + 3 $$ is $$ 2x^2 - 3x + 5 $$. To perform synthetic division of the polynomial $$ 2x^3 + 3x^2 - 4x + 15 $$ by $$ x + 3 $$, we first need to identify the root of the divisor $$ x + 3 $$. The root is $$ -3 $$. We will set up synthetic division using the coefficients of the polynomial: - The coefficients of $$ 2x^3 + 3x^2 - 4x + 15 $$ are $$ 2, 3, -4, 15 $$. Now, we set up the synthetic division: $$ \begin{array}{r|rrrr} -3 & 2 & 3 & -4 & 15 \ & & -6 & 9 & -15 \ \hline & 2 & -3 & 5 & 0 \ \end{array} $$ ### Steps: 1. Bring down the leading coefficient $$ 2 $$. 2. Multiply $$ -3 $$ (the root) by $$ 2 $$ (the number just brought down) to get $$ -6 $$, and write it under the next coefficient $$ 3 $$. 3. Add $$ 3 + (-6) = -3 $$. 4. Multiply $$ -3 $$ by $$ -3 $$ to get $$ 9 $$, and write it under the next coefficient $$ -4 $$. 5. Add $$ -4 + 9 = 5 $$. 6. Multiply $$ -3 $$ by $$ 5 $$ to get $$ -15 $$, and write it under the last coefficient $$ 15 $$. 7. Add $$ 15 + (-15) = 0 $$. The result of the synthetic division is: $$ 2x^2 - 3x + 5 $$ with a remainder of $$ 0 $$. Thus, the final result of dividing $$ 2x^3 + 3x^2 - 4x + 15 $$ by $$ x + 3 $$ is: $$ \boxed{2x^2 - 3x + 5} $$

Divide \( \left(2 x^{3}+3 x^{2}-4 x+15\right) \) by \( (x+3) \) using synthetic division

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Divide \( \left(2 x^{3}+3 x^{2}-4 x+15\right) \) by \( (x+3) \) using synthetic division

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