Answer
$3(x-2)(x-4)$
Work Step by Step
In order to factor $3x^{2}-18x+24$, we must first factor out a 3 (which is the greatest common factor of each term) from all three terms.
$3(x^{2}-6x+8)$
Next, we must find a pair of negative numbers whose product is equal to 8 (or the constant term) and whose sum is equal to -6 (or the coefficient on the middle term).
We know that the pairs of negative numbers whose product is 8 are -1,-8 and -2,-4.
Out of these pairs, the sum of -2 and -4 is equal to -6.
Therefore, $3x^{2}-18x+24=3(x-2)(x-4)$.
