Answer
$(w-2)(w+2)(w-3)$
Work Step by Step
$w^{3}-3w^{2}-4w+12$
Factor this expression by grouping. Begin by grouping the first two terms and the last two terms together:
$w^{3}-3w^{2}-4w+12=(w^{3}-3w^{2})-(4w-12)=...$
Take out common factor $w^{2}$ from the first parentheses and $4$ from the second parentheses:
$...=w^{2}(w-3)-4(w-3)=...$
Take out common factor $w-3$:
$...=(w^{2}-4)(w-3)=...$
Factor the difference of squares in the first parentheses. The formula for factoring an expression like this is $A^{2}-B^{2}=(A-B)(A+B)$. For the expression $A^{2}=w^{2}$ and $B^{2}=4$.
$...=(w-2)(w+2)(w-3)$
