Question

a) Show that x+1, x-2, and x + 3 are the factors of the polynomial p(x)=x^3 + 2x^2-5x-6.​

Answer 1

Answer:

As x+1, x-2, and x + 3 satisfy the polynomial p(x), hence they are the factor.

Step-by-step explanation:

Let $p(x)=x^3 + 2x^2-5x-6$

          $g(x)=x+1\\ \\ x=-1$

Now ,

        $p(-1)=(-1)^3+2(-1)^2-5(-1)-6\\ \\ p(-1)=-1+2+5-6=0$

Therefore,

           $x+1$ is the factor of $p(x)=x^3 + 2x^2-5x-6$

Again,

        $g(x)= x-2\\ \\ x=2$

Now,

           $p(2)=2^3+2(2^2)-5(2)-6\\ \\ p(2)=8+8-10-6=0$

Therefore,

          x-2 is the factor of p(x)

Again,

          $g(x)=x + 3\\ \\ x=-3$

Now,

       $p(-3)=(-3)^3+2(-3)^2-5(-3)-6\\ \\ p(-3)=-27+18+15-6=0$

Therefore,

                 x+3 is the factor of p(x)

Answer 2

Answer:

Step-by-step explanation:

X=-1,+2,-3

F(2)=2^3+2*2^2-5*2-6

=8+2*4-10-6

=8+8-10-6

0// SO 2 IS A ROOT

NOW X=-3

-27+2*3^2+15-6

-33+18+15

-33+33=0//

NOW -1

-1+2+5-6

+7-7+0// HOPE U GOT IT

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