Question

use the factor theorem to determine whether g(x) is a factor of p (x) in each of the following cases x⁴+x³+x²+x+1​

Answer 1

Step-by-step explanation:

Given polynomial f(x)=x

3

−4x

2

+x+6 the factor of g(x)=x−2

If x-2 is factor then x-2=0 or x=2

Replace x in p(x) by 2 we get

f(x)=x

3

−4x

2

+x+6

f(2)=(2)

3

−4(2)

2

+(2)+6

⇒f(2)=8−16+2+6

⇒f(2)=0

So f(x) is zero by g(x) =x-2 then g(x)=(x-2) is factor of f(x)=x

3

−4x

2

−x+6