Question

what is the factored form of x³-6x² + 3x + 10

Answer 1

Answer:

${x}^{3} - 6 {x}^{2} + 3x + 10 = (x + 1)(x - 2)(x - 5).$

Step-by-step explanation:

${x}^{3} - 6 {x}^{2} + 3x + 10 = {x}^{3} + {x}^{2} + 3 {x}^{2} + 3x - 10 {x}^{2} + 10 \\ \\ = {x}^{2} (x + 1) + 3x(x + 1) - 10( {x}^{2} - 1) \\ \\ = (x + 1)( {x}^{2} + 3x - 10(x - 1)) \\ \\ = (x + 1)( {x}^{2} - 7x + 10) \\ \\ = (x + 1)( {x }^{2} - 5x - 2x + 10) \\ \\ = (x + 1)(x(x -5 ) - 2(x - 5)) \\ \\ = (x + 1)(x - 2)(x - 5).$