Question

Xcube+6xsquare+11x+6 Factorise completely by factor theorem. how to do?

Answer 1

f(x)=x^3 +6x^2 +11x +6
value replace theorem
when x=-1;
f(-1)=(-1)^3 +6(-1)^2 +11(-1) +6
       = -1 +6 -11 +6
      =-12 +12
       =0//
f(x) =(x+1)(ax^2 +bx +c)
x^3 +6x^2 +11x +6 = ax^3 +x^2(b+a) +x(c+b)+c

x^3/                            x^2/                                     x^0/
1=a//..(1)                6=b+a                                      c=6//
                               6-1=b{ (1) equation }
                               5 =b
f(x)=(x+1)(x^2 +5x +6)
f(x)=(x+1)(x+2)(x+3)
factors are x+1 and x+3 and x+2//