Please Help! Which expression is a linear factor of x ^6 + x - 66? x + 1 x + 2 x + 4 none of the above

Question

asked Jan 17, 2017 219k views

2 Answers

Alloyoussef · Answer 1 · 2017-01-18T08:27:01+0000

Answer:

None of the above

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