Question

divide the polynomials. 12. $(3x^3 - 5x^2 - 6x + 2) \div (x + 1)$

Explanation:

Step1: Divide leading terms

$\frac{3x^3}{x} = 3x^2$

Step2: Multiply divisor by $3x^2$

$3x^2(x+1) = 3x^3 + 3x^2$

Step3: Subtract from dividend

$(3x^3 -5x^2 -6x +2) - (3x^3 +3x^2) = -8x^2 -6x +2$

Step4: Divide new leading terms

$\frac{-8x^2}{x} = -8x$

Step5: Multiply divisor by $-8x$

$-8x(x+1) = -8x^2 -8x$

Step6: Subtract from current polynomial

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

Step7: Divide new leading terms

$\frac{2x}{x} = 2$

Step8: Multiply divisor by 2

$2(x+1) = 2x +2$

Step9: Subtract to find remainder

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

Answer:

$3x^2 -8x +2$