Question

Factories x^3 -2x^2 -x+2

Answer 1

Hey mate here's ur answer

Answer 2

$\textsf{Let p(x) = x^3 - 2x^2 - x + 2 } \\ \\ \textsf{First we have to find any values for x which causes p(x) = 0 } \\ \\ \\ \textsf{Let x = 1 .} \\ \\ p(1) = 1^3 - 2(1)^2 - 1 + 2\\ \\ p(1) = 1 - 2 - 1 + 2 \\ \\ p(1) = 0 \\ \\ \\ \therefore\ \bold{1}\ \textsf{is a zero of p(x) . So (x - 1) is a factor.}$

$\textsf{Now we have to divide p(x) by (x - 1) .} \\ \\ \\ x^3 - 2x^2 - x + 2 \\ \\ x^3 - x^2 - x^2 + x - 2x + 2 \\ \\ x^2(x - 1) - x(x - 1) - 2(x - 1) \\ \\ (x - 1)(x^2 - x - 2) \\ \\ (x - 1)(x^2 + x - 2x - 2) \\ \\ (x - 1)(x(x + 1) - 2(x + 1)) \\ \\ (x - 1)(x + 1)(x - 2)\\ \\ \\ \therefore\ \ \Large x^3 - 2x^2 - x + 2 = (x - 1)(x + 1)(x - 2)$

$\textsf{We would get the answer easier on dividing p(x) by (x - 2) .} \\ \\ \\ x^3 - 2x^2 - x + 2 \\ \\ x^2(x - 2) - (x - 2) \\ \\ (x - 2)(x^2 - 1) \\ \\ (x - 2)(x + 1)(x - 1)$