Question

what is the completely factored form of $12xy - 9x - 8y + 6$?
$(3x - 2)(4y - 3)$
$3x(4y - 3) - 2(4y + 3)$
$-6x(4y - 3)(4y - 3)$
$(3x - 2)(4y - 3)(4y - 3)$

Explanation:

Step1: Group terms into pairs

Group first two and last two terms:
$(12xy - 9x) + (-8y + 6)$

Step2: Factor out GCF from each pair

Factor $3x$ from first pair, $-2$ from second pair:
$3x(4y - 3) - 2(4y - 3)$

Step3: Factor out common binomial

Factor $(4y - 3)$ from both terms:
$(3x - 2)(4y - 3)$

Step4: Verify non-factored options

Eliminate options that are not fully factored or incorrect. Option 2 is not fully factored; options 3 and 4 overfactor/have errors.

Answer:

(3x - 2)(4y - 3)