Question

A polynomial 6x^3 - 11x^2 + 21x - 2 was divided by 2x - 1 resulting in a quotient q(x) and remainder 3x + 5. Determine the quotient.

Answer 1

so we know that q(x) is a quadratic ax^2+bx+c. that means
(ax^2+bx+c)(2x-1) + 3x+5 = 6x^3 - 11x^2 + 21x - 2
2ax^3 + (2b-a)x^2 + (2c-b+3)x + (5-c) = 6x^3 - 11x^2 + 21x - 2
Now just equate coefficients and solve
2a = 6
2b-a = -11
2c-b+3 = 21
5-c = -2
q(x) = 3x^2 - 4x + 7