Question

How do you factor `1029yx^3 + 24y^4`?

Answer 1

`1029yx^3+24y^4=3y(343x^3+8y^3)`

`=3y((7x)^3+(2y)^3)`

`=3y(7x+2y)((7x)^2-(7x)(2y)+(2y)^2)`

`=3y(7x+2y)(49x^2-14xy+4y^2)`

using `a^3+b^3 = (a+b)(a^2-ab+b^2)`

There are linear factors of `(49x^2-14xy+2y^2)`, but they have Complex coefficients.