Question

1. $12w^2 - 13w - 4$

Explanation:

Step1: Find pair for AC method

Multiply $12 \times (-4) = -48$. Find two numbers that multiply to -48 and add to -13: -16 and 3.

Step2: Split middle term

Rewrite the expression by splitting $-13w$:
$12w^2 - 16w + 3w - 4$

Step3: Factor by grouping

Group first two and last two terms, factor out GCFs:
$4w(3w - 4) + 1(3w - 4)$

Step4: Factor common binomial

Factor out the shared $(3w - 4)$ term:
$(4w + 1)(3w - 4)$

Answer:

$(4w + 1)(3w - 4)$