Use the remainder theorem to find P(1) for P(x)=2x^3-3x^2-2x+3
Specifically, give the quotient and the remainder for the associated division and the value of P(1)
To find P(1) using the remainder theorem, we first divide the polynomial P(x) by (x-1) using long division or synthetic division.
2x^3 - 3x^2 - 2x + 3 divided by (x - 1)
The first step is to bring down the 2x^3 term:
2x^3 - 3x^2 - 2x + 3 | (x - 1)
(x - 1) | 2x^3 - 3x^2 - 2x + 3
-2x^3 + 2x^2
-------------
- x^2 - 2x
+ x^2 - x
---------------
-3
The quotient is 2x^2 + x and the remainder is -3.
Therefore, P(1) = 2(1)^3 - 3(1)^2 - 2(1) + 3
= 2 - 3 - 2 + 3
= 0
So, P(1) = 0.