Question

Factor completely:
x^10y^3 – 4x^9y^2 – 21x^8y

Answer 1

we can immediately take out an x^8 and a y^1
x^8 y ( x^2 y^2 - 4 x y - 21 )
21 = 3 * 7
3 - 7 = -4
so try
x^8 y ( x y - 7 ) ( x y + 3 )

Answer 2

Start by removing the common factor x^8 y.
x^10y^3 – 4x^9y^2 – 21x^8y
= x^8*y(x^2 y^2 -4 xy -21)
The term in parentheses is a quadratic in the variable xy, and can be factored to

(xy -7)(xy + 3).

Now put it all together

Answer 3

Thanks a lot, this really helps!