[tex]x^4-5x^3-42x^2+104x+320=0[/tex]
1) We are going to start with the factored form of a function. Given by this formula for a 4th-degree function:
[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]
In this question, the leading coefficient has been given to us already, so we can plug into that a=1
[tex]y=1(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]
2) Now let's plug into them the other roots:
[tex]y=(x+5_{})(x+2_{})(x-4_{})(x-8_{})[/tex]
2.2) Let's rewrite that function as an equation plugging y=0, and expanding it:
[tex]\begin{gathered} (x+5_{})(x+2_{})(x-4_{})(x-8_{})=0 \\ x^4-5x^3-42x^2+104x+320=0 \end{gathered}[/tex]
And that is the answer
