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Answer:

  • B. [tex]p^2+p-11[/tex].

Step-by-step explanation:

Step 1:

  • [tex]((((3+(4*(p^2)))-5p)-3p^2)+4p)+8[/tex]

Step 2:

  • [tex]((((3 + 22p^2) - 5p) - 3p^2) + 4p) + 8[/tex]

Step 3:

  • Factoring  [tex]p^2-p+11[/tex]
  • The first term is,  [tex]p^2[/tex]  its coefficient is  1 .
  • The middle term is,  -p  its coefficient is  -1 .
  • The last term, "the constant", is  +11
  • Step-1 : Multiply the coefficient of the first term by the constant   1 • 11 = 11
  • Step-2 : Find two factors of  11  whose sum equals the coefficient of the middle term, which is   -1 .
  •      -11    +    -1    =    -12
  •      -1    +    -11    =    -12
  •      1    +    11    =    12
  •      11    +    1    =    12
  • Observation : No two such factors can be found !!
  • Conclusion : Trinomial can not be factored

Final Solution:

  • [tex]p^2 + p - 11[/tex]

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