Question

1. factor $4x^2 - 10x + 2x - 5$ by grouping.

Explanation:

Step1: Group terms into pairs

Group the first two and last two terms:
$(4x^2 - 10x) + (2x - 5)$

Step2: Factor out GCF from each pair

Factor $2x$ from the first group, and 1 from the second group:
$2x(2x - 5) + 1(2x - 5)$

Step3: Factor out common binomial

Factor out the shared $(2x - 5)$ term:
$(2x - 5)(2x + 1)$

Answer:

$(2x - 5)(2x + 1)$