Question

use the factor theorm determine whether g(x) is a factor of p(x) = 3xpower4-4xpower3-3x-1 and g(x) = x+1​

Answer 1

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