1.

Factorise `x^(3)+6x^(2)+11x+6`.

Answer» Here, constant term=6
Its factors `=+-1,+-2,+-3, +-6`
Let `p(x)=x^(3)+6x^(2)+11x+6`
Put x=-1
`p(-1)=(-1)^(3)+6(-1)^(2)+11(-1)+6=-1+6-11+6=0`
`therefore x+1`, is a factor of p(x).
Now, `p(x)=x^(3)+6x^(2)+11x+6`
`x^(2)(x+1)+5x^(2)+11x+6`
`=x^(2)(x+1)+5x(x+1)+6x+6`
`=x^(2)(x+1)+5x(x+1)+6(x+1)`
`(x+1)(x^(2)+5x+6)`
`=(x+1)[x^(2)+2x+3x+6]`
`=(x+1)[x(x+2)+3(x+2)]`
=(x+1)(x+2)(x+3)


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