Question

1. factor $6x^2 + 3x + 2x + 1$ by grouping.

Explanation:

Step1: Group terms into pairs

Group the first two and last two terms:
$(6x^2 + 3x) + (2x + 1)$

Step2: Factor out GCF from each pair

Factor $3x$ from first group, 1 from second:
$3x(2x + 1) + 1(2x + 1)$

Step3: Factor out common binomial

Extract $(2x + 1)$ from both terms:
$(2x + 1)(3x + 1)$

Answer:

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