Question

using factor theorem check whether (x-3)is a factor of 3x4-8x3+13x2-15x+18​

Answer 1

Given polynomial f(x)=x3−4x2+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)=x3−4x2+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)=x3−4x2−x+6