Example Question - linear monomial division

Dividing a Cubic Polynomial by a Linear Monomial

Given \( P(x) = 2x^3 + 3x^2 - x - 5 \) and \( D(x) = x - 1 \), we will perform polynomial long division. \[ \begin{array}{r} 2x^2+5x+4 \\ x-1 \,|\overline{\, 2x^3 + 3x^2 - x - 5} \\ -\underline{2x^3 - 2x^2} \\ 5x^2 - x \\ -\underline{5x^2 - 5x} \\ 4x - 5 \\ -\underline{4x - 4} \\ -1 \end{array} \] The quotient is \( Q(x) = 2x^2 + 5x + 4 \) and the remainder is \( -1 \).