Question

Using factor theorm factorise x cube-2x square-5x+6

Answer 1

x³-2x²-5x+6
let x=1
1-2-5+6 ( after putting the value 1 in the given. polynomial )
=0
therefore, x-1 is the factor (1st)
x³-2x²-5x+6/x-1
=x²-x-6
factorising x²-x-6
=x²-3x+2x-6
=x(x-3)2(x-3)
(x+2)(x-3)
therefore the factors are x-1,x+2,x-3
hope this help....

Answer 2

${x}3 - 2 {x}2 - 5x + 6 = 0 \\ - x - 5x + 6 = 0 \\ - 6x + 6 = 0 \\ - 6x = - 6 \\ x = - 6 \div - 6 \\ x = 1$