Question

which of the following statements about $42xy - 49x + 30y - 35$ are true?
check all of the boxes that apply.
one of the factors is $(6y + 7)$.
one of the factors is $(7x + 5)$.
one of the factors is $(6y - 7)$.
one of the factors is $(7x - 5)$.
this expression is prime.

Explanation:

Step1: Group terms for factoring

Group first two and last two terms:
$(42xy - 49x) + (30y - 35)$

Step2: Factor out GCF from each group

Factor $7x$ from first group, $5$ from second group:
$7x(6y - 7) + 5(6y - 7)$

Step3: Factor out common binomial

Factor $(6y - 7)$ from both terms:
$(7x + 5)(6y - 7)$

Step4: Match with given options

Compare factored form to the listed factors.

Answer:

B. One of the factors is (7x + 5).
C. One of the factors is (6y - 7).