Question

find each quotient using

1. $(3n^3 - 3n^2 - 11n + 20) div (n + 2)$

Explanation:

Step1: Factor the cubic polynomial

We factor $3n^3 - 3n^2 - 11n + 20$. Using polynomial division or synthetic division with root $n=-2$ (since divisor is $n+2$):
$$3n^3 - 3n^2 - 11n + 20 = (n+2)(3n^2 - 9n + 5)$$

Step2: Cancel common factors

Divide the factored polynomial by $n+2$:
$$\frac{(n+2)(3n^2 - 9n + 5)}{n+2} = 3n^2 - 9n + 5$$

Answer:

$3n^2 - 9n + 5$