Question

use the factor theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i) p(x)=x^3+3x^2+3x+1,g(x)=x+1

Answer 1

If g(x) is a factor, then what happens if g(x) is zero?

p(x) will have 0 as a factor: p(x) becomes zero.

So we only have to make g(x) zero, then find if p(x) is also zero.

If p(x) doesn't have g(x) as a factor, p(x) won't become zero.

The required solution of g(x)=0 is x=-1.

Now we may apply the solution to p(x).

→ p(-1)=-1+3-3+1

→ p(-1)=0

Now g(x) is a factor of p(x), hence shown.

Answer 2

Answer:

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

Step-by-step explanation:

p(x)=x³+x²+3x+1

g(x)=>x+1=0

     =>x=-1

p(-1)=> (-1)³+(-1)²+3(-1)+1=0

     =>(-1)+1+(-3)+1=0

     =>-2≠0

∴g(x) is not a factor of p(x).