Answer:
(x - 3) is a factor of the given function
Step-by-step explanation:
Given function:
[tex]\implies f\:\!\:(x)=x^3-x^2-5x-3[/tex]
If (x - 3) is a factor of the given function then [tex]f\:\!\:(3) = 0[/tex]
Substitute x = 3 into the function and solve:
[tex]\implies f\:\!\:(3)=(3)^3-(3)^2-5(3)-3[/tex]
[tex]\implies f\:\!\:(3)=27-9-15-3[/tex]
[tex]\implies f\:\!\:(3)=0[/tex]
Therefore, as [tex]f\:\!\:(3) = 0[/tex] then (x - 3) is a factor of the given function.
