Question

1. perform long division on the following expression.

\frac{27x^{3}-39x - 26}{3x + 2}
type a response

Explanation:

Step1: Divide leading terms

$\frac{27x^3}{3x} = 9x^2$

Step2: Multiply divisor by result

$9x^2(3x+2) = 27x^3 + 18x^2$

Step3: Subtract from dividend

$(27x^3 - 39x - 26) - (27x^3 + 18x^2) = -18x^2 - 39x - 26$

Step4: Divide new leading terms

$\frac{-18x^2}{3x} = -6x$

Step5: Multiply divisor by result

$-6x(3x+2) = -18x^2 - 12x$

Step6: Subtract from current polynomial

$(-18x^2 - 39x - 26) - (-18x^2 - 12x) = -27x - 26$

Step7: Divide new leading terms

$\frac{-27x}{3x} = -9$

Step8: Multiply divisor by result

$-9(3x+2) = -27x - 18$

Step9: Subtract to find remainder

$(-27x - 26) - (-27x - 18) = -8$

Answer:

$9x^2 - 6x - 9 - \frac{8}{3x+2}$