SOLUTION: Use the Remainder Theorem to find P(-3) if P(x)= -2x^3+ x^2 -2x +11. Could you please show me all the work that is necessary to complete this problem so that I understand it com

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the Remainder Theorem to find P(-3) if P(x)= -2x^3+ x^2 -2x +11. Could you please show me all the work that is necessary to complete this problem so that I understand it com      Log On


   



Question 886911: Use the Remainder Theorem to find P(-3) if P(x)= -2x^3+ x^2 -2x +11.
Could you please show me all the work that is necessary to complete this problem so that I understand it completely and will know how it was done so I can do further problems similar to this. Thank you very much.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The idea is that the polynomial divided by x+3 gives the value of P(-3) as the remainder. Use synthetic division.


__________|___________________________
-3________|____-2_____1_____-2_____11
__________|___________6____-21_____69
_________________________________________
_______________-2_____7____-23_____80

The result is 80.
P(-3)=80.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Remainder Theorem to find P(-3) if P(x)= -2x^3+ x^2 -2x +11.
Could you please show me all the work that is necessary to complete this problem so that I understand it completely and will know how it was done so I can do further problems similar to this. Thank you very much.

P%28x%29+=+-+2x%5E3+%2B+x%5E2+-+2x+%2B+11
P%28-+3%29+=+-+2%28-+3%29%5E3+%2B+%28-+3%29%5E2+-+2%28-+3%29+%2B+11 ------- Substituting - 3 for x
P%28-+3%29+=+-+2%28-+27%29+%2B+9+%2B+6+%2B+11
P%28-+3%29+=+54+%2B+26
highlight_green%28highlight_green%28P%28-+3%29+=+80%29%29