Question

2 find the missing factor when rewriting $48ab^{3}-100ab^{2}+48ab$. $4ab(3b - 4)(?)$

Explanation:

Step1: Factor out GCF first

$48ab^3 - 100ab^2 + 48ab = 4ab(12b^2 - 25b + 12)$

Step2: Factor the quadratic trinomial

We need two terms that multiply to $12b^2$, and pairs of numbers that multiply to $12$, such that their cross products sum to $-25b$.
$12b^2 -25b +12 = (3b-4)(4b-3)$

Step3: Match given partial factorization

The given expression is $4ab(3b-4)(?)$, so the missing factor is the remaining binomial from factoring the quadratic.

Answer:

$4b - 3$