Question

if $f(x) = 2x^2 - 5x + 5$, then what is the remainder when $f(x)$ is divided by $x - 9$?

Explanation:

Step1: Recall Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( x - a \), the remainder is \( f(a) \). Here, we are dividing by \( x - 9 \), so \( a = 9 \). We need to find \( f(9) \).

Step2: Substitute \( x = 9 \) into \( f(x) \)

Given \( f(x) = 2x^2 - 5x + 5 \), substitute \( x = 9 \):
\[

$$\begin{align*} f(9) &= 2(9)^2 - 5(9) + 5 \\ &= 2(81) - 45 + 5 \\ &= 162 - 45 + 5 \\ &= 122 \end{align*}$$

\]

Answer:

122