Question

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

Answer 1

Step-by-step 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.