Question

Factorise :-x^3 + 6x² + 11x+6​

Answer 1

Answer:

(x+1)(x+1)(x+6)

Step-by-step explanation:

Given $x^{3} + 6x^{2} + 11x + 6$

Looking for the factors of 6, they are:

1,2,3,6,-1,-2,-3,-6

Put x= -1

p(1) = $(-1)^{3} + 6(-1)^{2} + 11(-1) +6$

$=-1 +6 -11+6\\=12-12\\=0$

So x= -1 is a zero of p(x)

So x+1 is a factor of p(x)

Now we will divide $x^{3} + 6x^{2} + 11x + 6$ by $x+1$

The quutioent is $x^{2} + 5x + 6$

Using splitting the middle term:-

$=x^{2} + 6x +x +6\\=x(x+1)+ 6(x+1)\\=(x+6)(x+1)$

Now, all the factors are:-

$(x+6)(x+1)(x+1)$