SOLUTION: if P^3+3P^2+3P=7, then the value of P^2+2P is

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Question 925979: if P^3+3P^2+3P=7, then the value of P^2+2P is
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The requested expression may have more than just one possible value, but at least this analysis works:

p%5E3%2B3p%5E2%2B3p-7=0
and testing of roots using Rational Roots Theorem and synthetic division shows....

_______1_____|_______1______3_______3______-7
_____________|
_____________|
_____________|_____________1_______4________7
__________________________________________________
____________________1______4_______7_________0


Note the remainder of 0.
The equation is %28p-1%29%28p%5E2%2B4p%2B7%29=0, with the found solution p=1.

You can use this to get a value for the expression p%5E2%2B2p.
1%5E2%2B2%2A1
highlight%283%29.

No other real value for p.
The quadratic factor is not factorable in real numbers.
(Discriminant is 4%2A4-4%2A7=16-28=-12%3C0 .)