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

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May 12, 2015

#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.

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