How do you factor $x^{3} + 15 x^{2} + 75 x + 125$ $x^3+15x^2+75x+125$ ?

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Answer 1 · 2015-05-27T23:11:12

$x^{3} + 125 = x^{3} + 5^{3} = (x + 5) (x^{2} - 5 x + 25)$ $color(red)(x^3+125 = x^3+5^3 = (x+5)(x^2-5x+25))$

$15 x^{2} + 75 x = (x + 5) (15 x)$ $color(blue)(15x^2+75x = (x+5)(15x))$

$x^{3} + 15 x^{2} + 75 x + 125$ $color(red)(x^3) + color(blue)(15x^2)+color(blue)(75x)+color(red)(125)$

Therefore:
$= (x^{3} + 125) + (15 x^{2} + 75)$ $=color(red)((x^3+125)) + color(blue)((15x^2+75))$

$= (x + 5) (x^{2} - 5 x + 25) + (x + 5) (15 x)$ $= (x+5)color(red)((x^2-5x+25)) + (x+5)color(blue)((15x))$

$= (x + 5) (x^{2} - 5 x + 25 + 15 x)$ $= (x+5)(color(red)(x^2-5x+25)+color(blue)(15x))$

$= (x + 5) (x^{2} + 10 x + 25)$ $=(x+5)(x^2+10x+25)$

$= {(x + 5)}^{3}$ $=(x+5)^3$

How do you factor x^3+15x^2+75x+125x3+15x2+75x+125x^3+15x^2+75x+125?