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