Question

Q-2 use the factor Theorem to determine
whether g (x.) is a factor of P(x) in each
of the following cases:p(x) =x³-4x²+x+6 ,g(x)=x-3​

Answer 1

Answer:

$g(x) = x - 3 \\ then \\ x = 3 \\ p(x) = x {}^{3} - 4x {}^{2} + x + 6 \\ p(3) = (3) {}^{3} - 4(3) {}^{2} + 3 + 6 \\ p(3) = 9 - 36 + 9 \\ p(3) = - 18$

Answer 2

Put x-3=0
x = 3
So p(3)=3^3-4(3)^2+3+6
=27-36+9
=0
Therefore g(x) is factor of p(x)