Question

use the factor theorem to determine whether g(x)is factor of f(x) in f(x)=x3-4x2+x+6,g(x)=x-2
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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)$x^{3} -4x^{2} +x+6$