Eli uses the factor theorem to determine whether x−2 is a factor of 6x5−22x2+11x−126.

the factor theorem states

(

x

−

a

)

is a factor of  

f

(

x

)

⇔

f

(

a

)

=

0

f

(

x

)

=

4

x

3

−

3

x

2

−

8

x

+

4

we have  

(

x

−

2

)

⇒

a

=

2

f

(

2

)

=

4

×

2

3

−

3

×

2

2

−

8

×

2

+

4

f

(

2

)

=

4

×

8

−

3

×

4

−

16

+

4

f

(

2

)

=

32

−

12

−

16

+

4

f

(

2

)

=

8

≠

0

∴

x

−

2

is not a factor of  

4

x

3

−

3

x

2

−

8

x

+

4

however by the remainder theorem when

f

(

x

)

=

4

x

3

−

3

x

2

−

8

x

+

4

is divided by  

(

x

−

2

)

the remainder is  

8

the factor theorem being a special case of the remainder theorem

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step-by-step explanation:

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if you explain the the question more correctly i might be able to answer this better

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