Question

if $f(x) = 3x^2 - 9x - 20$, find the value of $f(5)$ using synthetic division. -7 10 15 0

Explanation:

Step1: Identify coefficients and root

Coefficients: $3, -9, -20$; Root: $5$

Step2: Set up synthetic division

$$\begin{array}{r|rrr} 5 & 3 & -9 & -20 \\ \hline & & 15 & 30 \\ \hline & 3 & 6 & 10 \end{array}$$

Step3: Get remainder (f(5))

The final remainder is $10$, so $f(5)=10$

Answer:

10