Question

Use the factor theorem to determine whether g(x) is a factor of f(x) in each of the
following cases:
(i) f(x) = x3 - 3x2 + 4x - 4, g(x) = x - 2
(ii) f(x)=2.3x2 + 5x + V2, g(x)=x + 12​

Answer 1

Answer:

(i) g(x)=0

x-2=0

x=2

so,zero of g(x) is 2.

now,f(2)= (2)^3-3(2)^2+4(2)-4

=8-12+8-4

=-4+4

=0

therefore,by factor theorem,g(x) is a factor of f(x).

(ii)g(x)=0

x+12=0

x=-12

so zero of g(x) is -12.

now,f(-12)=2.3(-12)^2+5(-12)+(-12)^2

=331.2-60+144

=415.2