### Home > PC3 > Chapter 5 > Lesson 5.2.4 > Problem5-105

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 $(2,1)$.

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

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

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