Using factor theorem determine whether g(x) is a factor of p(x) P(x) =2x3 -11x2 -4x+1 g(x) =2x +1

g(x) is a factor of P(x).

Step-by-step explanation:

By the factor theorem, If g(a) = 0 and P(a) = 0, then g(x) is a factor of P(x).

Here

P(x) = 2x^3-11x^2-4x+1

g(x) = 2x + 1, g(-1/2) = 0

check

P(-1/2)

= 2(-1/2)^3-11(-1/2)^2-4(-1/2)x+1

=-1/4 - 11/4 + 2 + 1

= 0

Therefore g(x) is a factor of P(x).

As a matter of fact,

P(x) = ( 2x + 1 )( x^2 - 6x + 1 )

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.