Question

How do you solve this?

Answer 1

Note that 125 = 5³. Make use of the factorization of the sum of cubes:

a³ +b³ = (a+b)(a² -ab +b²) . . . . . . a formula worth keeping handy

Then ...

$\dfrac{x^3+5^3}{x+5}=\dfrac{(x+5)(x^2-5x+5^2)}{x+5}=x^2-5x+25$

_____

When x=-5, this evaluates to

... (-5)²-5(-5) +25 = 75

Answer 2

$\dfrac{x^3+125}{x+5}=\dfrac{(x+5)(x^2-5x+25)}{x+5}=x^2-5x+25\\\\ (-5)^2-5\cdot(-5)+25=25+25+25=75$