how would you factorise x^4+x
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x⁴ + x = x (x³ + 1)
Now (x³ + 1) is the sum of cubes.
Formulas for sum/difference of cubes:
a³ + b³ = (a + b) (a² − ab + b²)
a³ − b³ = (a − b) (a² + ab + b²)
x⁴ + x = x (x³ + 1)
x⁴ + x = x (x + 1) (x² − x + 1)
Now (x³ + 1) is the sum of cubes.
Formulas for sum/difference of cubes:
a³ + b³ = (a + b) (a² − ab + b²)
a³ − b³ = (a − b) (a² + ab + b²)
x⁴ + x = x (x³ + 1)
x⁴ + x = x (x + 1) (x² − x + 1)