Answer:
[tex](x-5)[/tex]
Step-by-step explanation:
The Factor Theorem tells us that substituting [tex]x=a[/tex] into a polynomial [tex]p(x)[/tex] when divided by a linear factor [tex](x-a)[/tex] will give us a value of 0 IF [tex](x-a)[/tex] is a factor of the polynomial [tex]p(x)[/tex]
So, checking each of the 4 binomials, and getting a 0 as answer will tell us which one is a factor of the function given.
Putting [tex]x=-1[/tex] for [tex](x+1)[/tex] into the function:
[tex]3(-1)^{3}-12(-1)^2-4(-1)-55\\=-66[/tex]
NOT a factor.
Putting [tex]x=-4[/tex] for [tex](x+4)[/tex] into the function:
[tex]3(-4)^{3}-12(-4)^2-4(-4)-55\\=-423[/tex]
NOT a factor.
Putting [tex]x=5[/tex] for [tex](x-5)[/tex] into the function:
[tex]3(5)^{3}-12(5)^2-4(5)-55\\=0[/tex]
IS a factor.
Putting [tex]x=2[/tex] for [tex](x-2)[/tex] into the function:
[tex]3(2)^{3}-12(2)^2-4(2)-55\\=-87[/tex]
NOT a factor.
So we can see that only [tex](x-5)[/tex] is a factor.
