Question

1. $6x^2 + 7x - 3$

Explanation:

Step1: Find pair for AC method

Multiply $6 \times (-3) = -18$. Find two numbers that multiply to -18 and add to 7: 9 and -2.

Step2: Split middle term

Rewrite the quadratic:
$6x^2 + 9x - 2x - 3$

Step3: Factor by grouping

Group terms and factor out GCFs:
$3x(2x + 3) - 1(2x + 3)$

Step4: Factor out common binomial

Extract the shared $(2x+3)$ term:
$(3x - 1)(2x + 3)$

Answer:

$(3x - 1)(2x + 3)$