Question

homework 5: polynomials
divide $\frac{n^{3}-5n^{2}+n+7}{n-1}$.
what is the remainder?

Explanation:

Step1: Apply Remainder Theorem

For polynomial $f(n)$ divided by $n-a$, remainder is $f(a)$. Here $a=1$.

Step2: Substitute $n=1$ into $f(n)$

$f(1) = 1^3 - 5(1)^2 + 1 + 7$

Step3: Calculate the value

$f(1) = 1 - 5 + 1 + 7 = 4$

Answer:

4