x4+12x3+21x2-98x=
x(x3+12x2+21x-98).
If we plug in x=2 (one of the factors of 98) we get:
2(8+48+42-98)=0 so x-2 is a factor.
Use synthetic division to find the quadratic:
2 | 1 12 21 -98
1 2 28 | 98
1 14 49 | 0 = x2+14x+49=(x+7)2.
So the final factorisation is x(x-2)(x+7)2.