Math Polynomial P(x) is divided by x-2. The quotient is 2x^2 + x-2 and the remainder is -1. Pre calc homework

Question

Math Polynomial P(x) is divided by x-2. The quotient is 2x^2 + x-2 and the remainder is -1. Find P(x).
Please show work if possible thanks for the help

Answer 1

P(x) = (x-2) (2x^2 + x-2 ) - 1

CHECK: Divide P(x) by (x-2);
quotient is (x-2) (2x^2 + x-2 ) / (x-2) or (2x^2 + x-2 )
Remainder: -1

Simplify:
P(x) = (x-2) (2x^2 + x-2 ) - 1
= x(2x^2) + x(x) + x(-2) - 2(2x^2) - 2(x) -2(-2) - 1
= 2x^3 + x^2 - 2x - 4x^2 - 2x + 4 - 1
= 2x^3 - 3x^2 - 4x + 3

Answer 2

[P(x) - (-1)]/(x-2) = ( 2x^2 + x - 2)

(x-2)(2x^2 + x - 2) = P(x) + 1

(x-2)(2x^2 + x - 2) -1 = P(x)

2x^3 + x^2 - 2x - 4x^2 - 2x + 4 - 1 = P(x)

2x^3 - 3x^2 - 4x + 3 = P(x)

Answer 3

p(x) = (2x^2 + x - 2)(x-2) - 1
= 2x^3 - 4x^2 + x^2 -2x -2x + 4 -1
= 2x^3 - 3x^2 - 4x + 3

Answer 4

P(x)/(x-2) = quotient + remainder

P(x)/(x-2) = 2x^2-1

P(x) = (x-2)(2x^2-1)

P(x) = 2x^3 - 4x^2 - x + 2