Answer:
None of the above
Step-by-step explanation:
We are given that an expression
[tex]x^6+x-66[/tex]
We have to find which expression is a linear factor of given expression.
1.[tex]x+1[/tex]
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
Factor theorem: if x+a is factor of polynomial P(x) then
P(a)=0=Remainder .
If p(a)=0 then x+a is a factor of p(x)
By factor theorem
[tex](-1)^6-1-66=-66\neq 0[/tex]
Hence, x+1 is not a linear factor of given expression.
2.[tex]x+2[/tex]
[tex]x=-2[/tex]
By factor theorem
[tex](-2)^6-2-66=64-2-66-4\neq 0[/tex]
Hence, x+2 is not a linear factor of given expression.
3.x+4
[tex]x=-4[/tex]
By factor theorem
[tex](-4)^6-4-66=4096-4-66=4026\neq [/tex]
Hence, x+4 is not a linear factor of given expression.
Answer: None of the above
