Question

x^3+2x^2+2x+1 how can i solve ​

Answer 1

p(x)=x³+2x²+2x+1

p(1)=(1)³+2(1)²+2(1)+1

=1+2+2+1

=6

p(-1)=(-1)³+2(-1)²+2(-1)+1

=-1+2-2+1

=0

hence x+1 is a factor of p(x)

p(x)=x³+2x²+2x+1

=x³+x²+x²+x+x+1

=x²(x+1)+x(x+1)+1(x+1)

=(x+1)(x²+x+1)

Answer 2

Answer:

(x+1)(x^2+x+1)

Step-by-step explanation:

Let p(x) = x^3+2x^2+2x+1

By trial and error method, we find that (-1) is a zero of p(x),

p(-1) = (-1)^3+2(-1)^2+2(-1)+1

      = (-1)+2(1)+(-2)+1

      = (-1)+2-2+1

      = 0

So, (x+1) is a factor of p(x).

By long division, we have,

x+1 )+x^3+2x^2+2x+1( x^2+x+1

      +x^3+  x^2

     (-)   (-)

_____________

              +x^2+2x+1

              +x^2+  x

             (-)    (-)

           ____________

                      +x+1

                     +x+1

                    (-) (-)

                 _________

                          0

Therefore,

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