If the expression $(125 - x^{3}) = (5 - x) (x^{2} + a x + b)$ , then the value of a is

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Solution

The correct option is D 5
We know that,
$125 - x^{3}$
$= 5^{3} - x^{3}$
$= (5 - x) [5^{2} + 5 x + x^{2}]$
$= (5 - x) [x^{2} + 5 x + 25] . . . . . . . . . . . . . . (1)$
But it is given that,
$125 - x^{3}$ $= (5 - x) [x^{2} + a x + b] . . . . . . . . . . . . . . (2)$
From (1) and (2) we get value of a is 5

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