Answer
$4z(x+2)(x+5)$
Work Step by Step
In order to factor $4x^{2}z+28xz+40z$, we must first factor out a 4z (which is the greatest common factor of each term) from all three terms.
$4z(x^{2}+7x+10)$
Next, we must find a pair of numbers whose product is equal to 10 (or the constant term) and whose sum is equal to 7 (or the coefficient on the middle term).
We know that the pairs of numbers whose product is 10 are 1,10 and 2,5.
Out of these pairs, the sum of 2 and 5 is equal to 7.
Therefore, $4x^{2}z+28xz+40z=4z(x+2)(x+5)$.
