Question

Check whether p(x) is factor of g(x):
i) p(x) = 3x3 + x2 +2x + 5 ; g(x) = 1 + x2 + 2x
ii) p(x) = – 9x + 2x4 + 3x3
– 12– 2x2
; g(x) = – 3 + x2

Answer 1

Answer:

Step-by-step explanation:

Given  

Check whether p(x) is factor of g(x): i) p(x) = 3x3 + x2 +2x + 5 ; g(x) = 1 + x2 + 2x ii) p(x) = – 9x + 2x4 + 3x3 – 12– 2x2 ; g(x) = – 3 + x2

ANSWER

We need to find whether g(x) is a factor of p(x). So consider

   g (x) = x^2 + 2 x + 1

              x^2 + x + x + 1 = 0

              x(x + 1) + 1(x + 1) = 0

                    x + 1 = 0

                      x = - 1

Substituting x = -1 in p(x) we get

         P(x) = 3(-1)^3 + (-1)^2 + 2(-1) + 5

                 = - 3 + 1 – 2 + 5

                = - 1

So p(x) is not equal to 0, hence g(x) is not a factor of p(x).

2. Now g(x) = x^2 – 3

         X^2 – 3 = 0

         x^2 = 3

          x^2 = ± 3

Now substituting x = 3 in p(x) we get

 P(x) = - 9x + 2 x^4 + 3 x^3 – 12 – 2 x^2

        = - 9(3) + 2(3)^4 + 3(3)^3 – 12 – 2(3)^2

       = - 27 + 162 + 81 – 12 – 18

        = 186

Again x = - 3

P(x) = - 9(-3) + 2(-3)^4 + 3(- 3)^3 – 12 – 2(- 3)^2

       = 27 + 162 – 81 – 12 – 18

      = 78

So g(x) is not a factor of p(x) since p(x) is not equal to zero.