Question

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

Explanation:

Step1: Apply Remainder Theorem

For polynomial $f(x)$ divided by $x-a$, remainder is $f(a)$. Here divisor is $x+1=x-(-1)$, so $a=-1$.

Step2: Evaluate $f(-1)$

Given $f(x)=x^2-3x+5$, substitute $x=-1$:
$$f(-1)=(-1)^2 - 3(-1) + 5$$

Step3: Calculate the value

$$f(-1)=1 + 3 + 5 = 9$$

Answer:

9