Question

please answer

use the factor theorem to determine whether g (x) is the factor of p (x) in each of the following cases​

Answer 1

Answer:

Step-by-step explanation:

Ans.

(i)  We know that according to the factor theorem,

We can conclude that g(x) is a factor of p(x), if p(-1)=0.

= 2+1-1-2 = 0

Therefore, we conclude that the g(x) is a factor of p(x).

(ii) We know that according to the factor theorem,

We can conclude that g(x) is a factor of p(x), if p(-2)=0.

= -8+12-6+1 = -1

Therefore, we conclude that the g(x) is not a factor of p(x).

(iii)  We know that according to the factor theorem,

We can conclude that g(x) is a factor of p(x), if p(3)=0.

= 27-36+3+6 = 0

Therefore, we conclude that the g(x) is a factor of p(x).

Answer 2

Answer:

Put g(x) = 0

X+1=0

X= - 1

By remainder theorem

Remainder=p(-1)

P(x) =2x^3 +x^2 - 2x - 1

= 2× (-1)^3 + (-1)^2 - 2× - 1 +1

= 2× - 1 + 1 +2 +1

= - 2 +2+3

=3

I think it is right