Simplify x3 + 15x2 + 75x + 125/x2 - 25 (x - 5). - SSC STUDY

Simplify $\dfrac{x^3 + 15x^2 + 75x + 125}{x^2 - 25} (x - 5)$ .

Options
a) x² + 5x + 25
b) x² – 25
c) x² + 10x + 25
d) x² + 25

Solution

As per question
$\dfrac{x^3 + 15x^2 + 75x + 125}{x^2 - 25} (x - 5)$

$\dfrac{x^3 + 15x^2 + 75x + 125 (x - 5)}{(x - 5)(x + 5)}$

$\dfrac{(x +5)^2 (x + 5)}{x + 5}$
(x + 5)² = x² + 10x + 25

Ans is ) x² + 10x + 25