How do you factor x to the third power plus 125?

Answer 1

x^(3) + 125

= (x^3) + (5^3)

This factors into

(x + 5){x^(2) - 5x + 5^(2) }

= (x + 5)(x^(2) - 5x + 25)

The clue is to recognize that the constant (125) is a cubic number (5^3).

Answer 2

x^(3) + 125 =>

x^(3) + 5^(3)

This factors to

(x + 5)(x^(2) - 5x + 5^(2) ) or (x + 5)(x^(2) - 5x + 25)

NB The clue is to spot that the constant (125) is a cubic numbers ( 5^(3)).

Similarly with other 'cubic factorings'.

Answer 3

(x + 5)(x^2 - 5x + 25)

Answer 4

x3 + 125 = (x + 5)(x2 - 5x + 25)