Question

Q.6
Use the factor theorem todetermine whether g(x) is a factor of p(x) in the following:
P(x) =x3+3x2+3x+1,g(x)=x+2

​

Answer 1

Let p(x) = x^3 + 3x^2 + 3x + 1;

If g(x) is a factor of p(x), then by factor theorem, p(-2) should be equal to zero.

Hence,

p(-2) = (-2)^3 + 3(-2)^2 + 3(-2) +1

= -8 + 12 - 6 + 1

= 13 - 14

= -1 which is not equal to 0

Thus, g(x) is not a factor of p(x).

HOPE THIS COULD HELP!!!