The remainder when `P(x) = ax^3 + bx +c`  is divided by`x+1, x-1`  and `x-2 ` are 4, 0 and 4 respectively. Find the values of a, b, c and P(x).

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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We can use the remainder theorem here.

It says when f(x) is divided by (x-a) then the remainder is given by f(a).

Using the given data;

`P(-1) = a(-1)^3+b(-1)+c = 4 => -a-b+c = 4---(1)`

`P(1) = a(1)+b(1)+c = 0 => a+b+c = 0 ---(2)`

`P(2) = a(2)^3+b(2)+c = 4 => 8a+2b+c = 4 -----(3)`

By solving (1),(2) and (3) we will get;

`a = 1`

`b = -3`

`c = 2`

So the answer are as follows.

`a = 1`

`b = -3`

`c = 2`

`P(x) = x^3-3x+2`

Sources:

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