Use the factor theorem to determine whether g(x) =x+1 is a factor of p(x) in the following p(x) =2x^3+x^2 -2x -1​

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1. Explanation:

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2. Explanation:

   (i) Apply factor theorem

   x+1=0

   So x=−1

   2x

   3

   +x

   2

   −2x−1

   Replace x by −1, we get

   2(−1)

   3

   +(−1)

   2

   −2(−1)−1=−2+1+2−1=0

   Reminder is 0 so that x+1 is a factor of 2x

   3

   +x

   2

   −2x−1

   (ii) Apply factor theorem

   x+2=0

   So x=−2

   x

   3

   +3x

   2

   +3x+1

   Replace x by −2, we get

   (−2)

   3

   +3(−2)

   2

   +3(−2)+1=−8+12−6+1=1

   Reminder is 1 so that x+2 is not a factor of x

   3

   +3x

   2

   +3x+1

   (iii) Apply factor theorem

   x−3=0

   So x=3

   x

   3

   −4x

   2

   +x+6

   Replace x by 3, we get

   (3)

   3

   −4(3)

   2

   +(3)−1=27−36+3+6=0

   Reminder is 0 so that x−3 is a factor of x

   3

   −4x

   2

   +x+6

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