(2x³ + 5x² + 9) ÷ (x + 3)

Answer

Explanation:

Step1: Polynomial long division

Divide (2x^{3}+5x^{2}+9) by (x + 3). First, divide (2x^{3}) by (x) to get (2x^{2}). Multiply (x + 3) by (2x^{2}) gives (2x^{3}+6x^{2}). Subtract this from (2x^{3}+5x^{2}+9) to get (-x^{2}+9).

Step2: Continue division

Divide (-x^{2}) by (x) to get (-x). Multiply (x + 3) by (-x) gives (-x^{2}-3x). Subtract this from (-x^{2}+9) to get (3x + 9).

Step3: Final division

Divide (3x) by (x) to get (3). Multiply (x + 3) by (3) gives (3x+9). Subtract this from (3x + 9) gives (0).

Answer:

(2x^{2}-x + 3)