Question

(2x³ + 5x² + 9) ÷ (x + 3)
2x² - x + 3
2x² + 11x + 33 + 108/(x+3)
2x² - 5x + 12
2x³ - x² + 3x

Explanation:

Step1: Polynomial long division setup

Divide $2x^3 + 5x^2 + 9$ 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 remaining term

New dividend: $-x^2 + 9$

Step5: Divide leading terms

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

Step6: Subtract from new dividend

$(-x^2+9)-(-x^2-3x) = 3x + 9$

Step7: Divide leading terms

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

Step8: Subtract to find remainder

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

Step9: Combine quotient terms

$2x^2 - x + 3$

Answer:

$2x^2 - x + 3$