Question

heya
pls factorize with steps-
x^3-y^3+3xy+1

Answer 1

At first glance (0,1)(0,1) and (1,0)(1,0) are solutions. If it has a nice linear solution, fitting this then that would be y=−x+1y=−x+1, lets plug it in:

x3+3x(−x+1)+(−x+1)3−1=x−3x2+3x+1−x2+3x2–3x+1–1=0x3+3x(−x+1)+(−x+1)3−1=x−3x2+3x+1−x2+3x2–3x+1–1=0

Well, then lets try to factor out y+x−1y+x−1 using the usual polynomial division first decreasing the order in x then in y:

x3+3xy+y3–1:x+y−1=x2+x−xy+y2+y−1x3+3xy+y3–1:x+y−1=x2+x−xy+y2+y−1

So a factorization is:

x3+3xy+y3–1=(x+y−1)(x2+x−xy+y2+y−1)





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