Question

(2x³ + 5x² + 9) ÷ (x + 3)

1. 2x² - x + 3
2. 2x² + 11x + 33 + 108/(x+3)
3. 2x² - 5x + 12
4. 2x³ - x² + 3x

Explanation:

Step1: Set up polynomial long division

Divide $2x^3+5x^2+0x+9$ by $x+3$

Step2: Divide leading terms

$\frac{2x^3}{x}=2x^2$, multiply divisor: $2x^2(x+3)=2x^3+6x^2$

Step3: Subtract from dividend

$(2x^3+5x^2)-(2x^3+6x^2)=-x^2$

Step4: Bring down next term

New dividend: $-x^2+0x$

Step5: Divide leading terms

$\frac{-x^2}{x}=-x$, multiply divisor: $-x(x+3)=-x^2-3x$

Step6: Subtract from new dividend

$(-x^2+0x)-(-x^2-3x)=3x$

Step7: Bring down final term

New dividend: $3x+9$

Step8: Divide leading terms

$\frac{3x}{x}=3$, multiply divisor: $3(x+3)=3x+9$

Step9: Subtract to find remainder

$(3x+9)-(3x+9)=0$

Step10: Combine quotient terms

$2x^2 - x + 3$

Answer:

$2x^{2}-x+3$