Question

(2x³ + 7x² - 6x - 8) ÷ (x + 4)
options:
2x³ - x² - 2x
2x³ + 15x² + 54x + 208
2x² + 15x + 54 + 208/(x+4)
2x² - x - 2

Explanation:

Step1: Polynomial long division setup

Divide $2x^3 + 7x^2 - 6x - 8$ by $x+4$

Step2: Divide leading terms

$\frac{2x^3}{x} = 2x^2$, multiply divisor: $2x^2(x+4)=2x^3+8x^2$

Step3: Subtract from dividend

$(2x^3+7x^2-6x-8)-(2x^3+8x^2)=-x^2-6x-8$

Step4: Divide new leading terms

$\frac{-x^2}{x}=-x$, multiply divisor: $-x(x+4)=-x^2-4x$

Step5: Subtract from new dividend

$(-x^2-6x-8)-(-x^2-4x)=-2x-8$

Step6: Divide final leading terms

$\frac{-2x}{x}=-2$, multiply divisor: $-2(x+4)=-2x-8$

Step7: Subtract to find remainder

$(-2x-8)-(-2x-8)=0$

Step8: Combine quotient terms

$2x^2 - x - 2$

Answer:

$2x^2 - x - 2$