Question

use synthetic division to simplify \\(\frac{x^2 + 12x - 11}{x - 1}\\).
write your answer in the form \\(q(x) + \frac{r}{d(x)}\\), where \\(q(x)\\) is a polynomial, \\(r\\) is an integer, and \\(d(x)\\) is a linear polynomial. simplify any fractions.

Explanation:

3: Perform synthetic division
Bring down 1. Multiply by 1: $1×1=1$. Add to 12: $12+1=13$. Multiply by1: $13×1=13$. Add to -11: $-11+13=2$.

Step4: Form result

Quotient: $x + 13$, remainder: $2$. So $\frac{x²+12x-11}{x-1}=x+13+\frac{2}{x-1}$.

Answer:

3: Perform synthetic division
Bring down 1. Multiply by 1: $1×1=1$. Add to 12: $12+1=13$. Multiply by1: $13×1=13$. Add to -11: $-11+13=2$.

Step4: Form result

Quotient: $x + 13$, remainder: $2$. So $\frac{x²+12x-11}{x-1}=x+13+\frac{2}{x-1}$.