Question

week 7
use synthetic substitution to evaluate the following function. (hint: use long division. your answer is simply the remainder! they will be large numbers)
f(x)=2x^{3}-5x^{2}-x + 14
f(4)=
f(-2)=

Explanation:

Step1: Evaluate $f(-2)$

Substitute $x = - 2$ into $f(x)=2x^{3}-5x^{2}-x + 14$.
\[

$$\begin{align*} f(-2)&=2(-2)^{3}-5(-2)^{2}-(-2)+14\\ &=2\times(-8)-5\times4 + 2+14\\ &=-16-20 + 2+14\\ &=-20 \end{align*}$$

\]

Step2: Evaluate $f(4)$

Substitute $x = 4$ into $f(x)=2x^{3}-5x^{2}-x + 14$.
\[

$$\begin{align*} f(4)&=2\times4^{3}-5\times4^{2}-4 + 14\\ &=2\times64-5\times16-4 + 14\\ &=128-80-4 + 14\\ &=58 \end{align*}$$

\]

Answer:

$f(-2)=-20$
$f(4)=58$