Question
Factorize:
$x^3 + x - 3x^2 - 3$
$x^3 + x - 3x^2 - 3$
✓
Answer
$x^3 + x - 3x^2 - 3$
Taking x common in $x^3 + x$
$= x(x^2 + 1) - 3x^2 - 3$
Taking -3 common in $-3x^2 - 3$
$= x(x^2 + 1) - 3(x^2 + 1)$
Now,
we take $(x^2+ 1)$ common
$= (x^2 + 1)(x - 3)$
$\therefore$ $x^3 + x - 3y^2 - 3$
$= (x^2 + 1)(x - 3)$
Taking x common in $x^3 + x$
$= x(x^2 + 1) - 3x^2 - 3$
Taking -3 common in $-3x^2 - 3$
$= x(x^2 + 1) - 3(x^2 + 1)$
Now,
we take $(x^2+ 1)$ common
$= (x^2 + 1)(x - 3)$
$\therefore$ $x^3 + x - 3y^2 - 3$
$= (x^2 + 1)(x - 3)$
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