x³ - 8x² + 17x - 10

let p(x)= x³-8x²+17x-10

Putting x=1 in p(x) we get 0

therefore x-1 is a factor of p(x)

now  x³-8x²+17x-10 can be written as

=x³-x²-7x²+7x+10x-10 

=x²(x-1)-7x(x-1)+10(x-1)            

=(x-1){x²-7x+10}             (taking x-1 common)

=(x-1){x²+5x+2x+10}      (Factorising)

=(x-1){x(x+5)+2(x+5)}

=(x-1)(x+2)(x+5)

=x³-x²-7x²+7x+10x-10

=x²(x-1)-7x(x-1)+10(x-1)

=(x-1){x²-7x+10} (taking x-1 common)

=(x-1){x²+5x+2x+10} (Factorising)

=(x-1){x(x+5)+2(x+5)}

=(x-1)(x+2)(x+5)