Answer:
None of the above
Step-by-step explanation:
We are given that an expression
\(x^6+x-66\)
We have to find which expression is a linear factor of given expression.
1.\(x+1\)
\(x+1=0\)
\(x=-1\)
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
\((-1)^6-1-66=-66
eq 0\)
Hence, x+1 is not a linear factor of given expression.
2.\(x+2\)
\(x=-2\)
By factor theorem
\((-2)^6-2-66=64-2-66-4
eq 0\)
Hence, x+2 is not a linear factor of given expression.
3.x+4
\(x=-4\)
By factor theorem
\((-4)^6-4-66=4096-4-66=4026
eq\)
Hence, x+4 is not a linear factor of given expression.
Answer: None of the above
