Factorise -

x³- 9x²+6x +56

let p(x)= x³-9x²+6x+56 we first try to find a factor of p(x) .. we get

g(x)= x+2 as the factor of p(x) .. let's check

p(-2)= -8-36-12+56 = 0

now we do long divison of p(x) by g(x)

we get as x²-11x+28 quotient

now we have,

p(x)= (x+2)(x²-11x+28)

= (x+2)(x²-7x-4x+28) [By middle term splitting]

=(x+2)[x(x-7)-4(x-7)]

=(x+2)(x-7)(x-4) -Ans