Question

Using the remainder theorem find factorise 2x^3-13x^2+26x-15

Answer 1

${2x}^{2} - {13x}^{2} + 26x - 15 \\ = {2x}^{2} - {2x}^{2} - {11x}^{2} + 11x + 15x + 15 \\ = {2x}^{2} (x - 1) - 11x(x - 1) + 15(x - 1) \\ = (x - 1)( {2x}^{2} - 11x + 15) \\ = (x - 1)(x(2x - 5) - 3(2x - 5)) \\ = (x - 1)( 2x - 5)(x - 3)$