Question

What is the answer of
k³+6k²+9k+4??

Answer 1

DONE BY USING VANISHING METHOD
Let f(k)=k³+6k²+9k+4
then, f(-1)= (-1)³+6×(-1)²+9×(-1)+4
                = (-1)+6-9+4
                = 5-5
                =0
Since f(-1)=0 therefore (k+1) is a factor of f(k)
therefore, k³+6k²+9k+4
                =k³+k²+5k²+5k+4k+4
                =k²(k+1)+5k(k+1)+4(k+1)
                =(k+1) (k²+5k+4)
the answer is (k+1) (k²+5k+4).