Question

How do I find the zeros using synthetic division when the highest degree is 4

Answer 1

Answer:

Explanation:

Given f(x) defined below:

$f\mleft(x\mright)=x^4-11x^3+40x^2-48x$

To find the zeros, set f(x) equal to 0.

$x^4-11x^3+40x^2-48x=0$

First, observe that we can factor out x.

$\begin{gathered} x(x^3-11x^2+40x-48)=0 \\ \implies x=0\text{ or }x^3-11x^2+40x-48=0 \end{gathered}$

Given that x=3 is a zero of the function, we divide using synthetic division to find the other factors.