Question

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

1. 3x² - 5x - 2 + 8/(x + 1)
2. 3x³ - 5x² - 2x + 8
3. 3x³ + x² - 6x
4. 3x² + x - 6

Explanation:

Step1: Set up polynomial division

Divide $3x^3 - 2x^2 -7x +6$ by $x+1$

Step2: Divide leading terms

$\frac{3x^3}{x} = 3x^2$. Multiply $x+1$ by $3x^2$: $3x^3 +3x^2$

Step3: Subtract from dividend

$(3x^3 -2x^2) - (3x^3 +3x^2) = -5x^2$. Bring down $-7x$: $-5x^2 -7x$

Step4: Divide new leading terms

$\frac{-5x^2}{x} = -5x$. Multiply $x+1$ by $-5x$: $-5x^2 -5x$

Step5: Subtract again

$(-5x^2 -7x) - (-5x^2 -5x) = -2x$. Bring down $6$: $-2x +6$

Step6: Divide leading terms again

$\frac{-2x}{x} = -2$. Multiply $x+1$ by $-2$: $-2x -2$

Step7: Find remainder

$(-2x +6) - (-2x -2) = 8$

Step8: Write final result

Quotient + $\frac{\text{Remainder}}{\text{Divisor}}$: $3x^2 -5x -2 + \frac{8}{x+1}$

Answer:

A. $3x^2 - 5x - 2 + \frac{8}{x+1}$