CPM Homework Help : PC3 Problem 5-105

Write an equation for a fourth-degree polynomial function that has roots at $x=2\pm i$ , $x=3$ , $x=−4$ , and passes through the point $(2,1)$ .

Hint:

If $x=c$ is a root, then $(x−c)$ is a factor.

Step:

$p\left(x\right)=a\left(x-\left(2+i\right)\right)\left(x-\left(2-i\right)\right)\left(x-3\right)\left(x-\left(-4\right)\right)$

More Help:

Use the point $(2,1)$ to solve for the value of $a$ .