Questions: Use polynomial long division to rewrite the following fraction in the form q(x)+r(x)/d(x), where d(x) r(x) is the remainder. (x^3+7x^2-18x-6)/(x-2)

Solution Steps

To solve this problem using polynomial long division, we need to divide the polynomial $x^3 + 7x^2 - 18x - 6$ by $x - 2$. The result will be in the form $q(x) + \frac{r(x)}{d(x)}$, where $q(x)$ is the quotient and $r(x)$ is the remainder.

We start with the polynomial $P(x) = x^3 + 7x^2 - 18x - 6$ and divide it by $D(x) = x - 2$. Using polynomial long division, we find the quotient and remainder.

The quotient obtained from the division is $Q(x) = x^2 + 9x + 0$. This simplifies to $Q(x) = x^2 + 9x$.

The remainder from the division is $R(x) = -6$.

Final Answer